stability analysis of lattice boltzmann methods the lattice boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered although the equation is a derivative of lattice gas automata it may be interpreted as a lagrangian finite difference method for the numerical simulation of the discrete velocity boltzmann equation that makes use of a bgk collision operator as a result it is not surprising that numerical instability of lattice boltzmann methods have been frequently encountered by researchers we present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant density uniform mean flow the linear stability depends on the following parameters the distribution of the mass at a site between the different discrete speeds the bgk relaxation time the mean velocity and the wavenumber of the perturbations this parameter space is too large to compute the complete stability characteristics we report some stability results for a subset of the parameter space for a 7 velocity hexagonal lattice a 9 velocity square lattice and a 15 velocity cubic lattice results common to all three lattices are 1 the bgk relaxation time must be greater than 12 corresponding to positive shear viscosity 2 there exists a maximum stable mean velocity for fixed values of the other parameters and 3 as is increased from 12 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger

applications of field theoretic renormalization group methods to reaction diffusion problems we review the application of field theoretic renormalization group rg methods to the study of fluctuations in reaction diffusion problems we first investigate the physical origin of universality in these systems before comparing rg methods to other available analytic techniques including exact solutions and smoluchowski type approximations starting from the microscopic reaction diffusion master equation we then pedagogically detail the mapping to a field theory for the single species reaction ka a k we employ this particularly simple but non trivial system to introduce the field theoretic rg tools including the diagrammatic perturbation expansion renormalization and callan symanzik rg flow equation we demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative dc d expansions with respect to the upper critical dimension dc with these basics established we then provide an overview of more sophisticated applications to multiple species reactions disorder effects l evy flights persistence problems and the influence of spatial boundaries we also analyse field theoretic approaches to non equilibrium phase transitions separating active from absorbing states we focus particularly on the generic directed percolation universality class as well as on the most prominent exception to this class even offspring branching and annihilating random walks finally we summarize the state of the field and present our perspective on outstanding problems for the future

three state cyclic voter model extended with potts energy the cyclically dominated voter model on a square is extended by taking into consideration the variation of potts energy during the nearest neighbor invasions we have investigated the effect of surface tension on the self organizing patterns maintained by the cyclic invasions a geometrical analysis is also developed to study the three color patterns these investigations clearly indicate that in the voter model limit the pattern evolution is governed by the loop creation due to the overhanging during the interfacial roughening conversely in the presence of surface tension the evolution is governed by spiral formation whose geometrical parameters depend on the strength of cyclic dominance

similarity based cooperation and spatial segregation we analyze a cooperative game where the cooperative act is not based on the previous behavior of the coplayer but on the similarity between the players this system has been studied in a mean field description recently phys rev e 68 046129 2003 here the spatial extension to a two dimensional lattice is studied where each player interacts with eight players in a moore neighborhood the system shows a strong segregation independent of parameters the introduction of a local conversion mechanism towards tolerance allows for four state cycles and the emergence of spiral waves in the spatial game in the case of asymmetric costs of cooperation a rich variety of complex behavior is observed depending on both cooperation costs finally we study the stabilization of a cooperative fixed point of a forecast rule in the symmetric game which corresponds to cooperation across segregation borders this fixed point becomes unstable for high cooperation costs but can be stabilized by a linear feedback mechanism

least squares based lattice boltzmann method a meshless approach for simulation of flows with complex geometry a version of lattice boltzmann method lbm is presented in this work which is derived from the standard lbm by using taylor series expansion and optimized by the least squares method the method is basically meshless and can be applied to any complex geometry and nonuniform grids it can also be applied to different lattice models the proposed method explicitly updates the distribution functions at mesh points by an algebraic formulation in which the relevant coefficients are precomputed from the coordinates of mesh points we have successfully applied this method to simulate many two dimensional incompressible viscous flows the numerical results are very accurate and the computational time needed is much less as compared with other existing methods in this paper we mainly show the method

simulating time harmonic flows with the lattice boltzmann method we simulate time harmonic flows by the lattice boltzmann method we propose a general scheme to choose simulation parameters under the constraints of fixed reynolds and womersley numbers and with a specified simulation error under these constraints parameters are chosen to minimize the execution time numerical stability is studied in a range of reynolds and womersley numbers as an example of time harmonic flow simulations results of blood flow in a human abdominal aorta are presented

parity law for population dynamics of n species with cyclic advantage competitions we study population dynamics on lattice space with n species n 3 4 5 and 6 with cyclic competitive advantage having both a weaker species and a stronger one the steady state with equal population densities is the globally stable fixed point for the biased rate cyclic advantage population we can observe the different features of the steady states and their stabilities for even n and for odd n and we call it as parity law we obtain the following results on the parity law i for odd number n all the species can coexist following the biased rate and we have the counterintuition for the change of equilibrium densities ii for even n all the species cannot always coexist and it coincides with our intuition we also analyzed mean field approximation it is revealed that most of the results of monte carlo simulation can be understood by mean field approximation dynamics however equilibrium densities cannot be always predicted by mean field approximation because of the spatial fixation

a new differential lattice boltzmann equation and its application to simulate incompressible flows on non uniform grids a new differential lattice boltzmann equation lbe is presented in this work which is derived from the standard lbe by using taylor series expansion only in spatial direction with truncation to the second order derivatives the obtained differential equation is not a wave like equation when a uniform grid is used the new differential lbe can be exactly reduced to the standard lbe the new differential lbe can be applied to solve irregular problems with the help of coordinate transformation the present scheme inherits the merits of the standard lbe the 2 d driven cavity flow is chosen as a test case to validate the present method favorable results are obtained and indicate that the present scheme has good prospects in practical applications

defensive alliances in spatial models of cyclical population interactions as a generalization of the three strategy rock scissors paper game dynamics in space cyclical interaction models of six mutating species are studied on a square lattice in which each species is supposed to have two dominant two subordinated and a neutral interacting partner depending on their interaction topologies all imaginable systems can be classified into four isomorphic groups exhibiting significantly different behaviors as a function of mutation rate in three out of four cases three or four species form defensive alliances that maintain themselves in a self organizing polydomain structure via cyclic invasions varying the mutation rate this mechanism results in an ordering phenomenon analogous to that of magnetic ising systems the model explains a very basic mechanism of community organization which might gain important applications in biology economics and sociology

cyclical interactions with alliance specific heterogeneous invasion rates we study a six species lotka volterra type system on different two dimensional lattices when each species has two superior and two inferior partners the invasion rates from predator sites to a randomly chosen neighboring prey site depend on the predator prey pair whereby cyclic symmetries within the two three species defensive alliances are conserved monte carlo simulations reveal an unexpected nonmonotonous dependence of alliance survival on the difference of alliance specific invasion rates this behavior is qualitatively reproduced by a four point mean field approximation the study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences

hydrodynamic behavior of lattice boltzmann and lattice bhatnagar gross krook models we present a numerical analysis of the ranges of validity of classical and generalized hydrodynamics for lattice boltzmann and lattice bhatnagar gross krook bgk methods in two and three dimensions as a function of the collision parameters of these models our analysis is based on the wave number dependence of the evolution operator good ranges of validity are found as long as the bgk relaxation time is chosen smaller than or equal to unity the additional degree of freedom in a two parameter bgk model can give further improvements

estimation risk for the var of portfolios driven by semi parametric multivariate models abstract joint estimation of market and estimation risks in portfolios is investigated when the individual returns follow a semi parametric multivariate dynamic model and the asset composition is time varying under ellipticity of the conditional distribution asymptotic theory for the estimation of the conditional value at risk var is developed an alternative method the filtered historical simulation which does not rely on ellipticity is also studied asymptotic confidence intervals for the conditional var which allow for simultaneous quantification of the market and estimation risks are derived the particular case of minimum variance portfolios is analyzed in more detail potential usefulness feasibility and drawbacks of the two approaches are illustrated via monte carlo experiments and an empirical study based on stock returns

zero one survival behavior of cyclically competing species the coexistence of competing species is due to unavoidable fluctuations always transient in this letter we investigate the ultimate survival probabilities characterizing different species in cyclic competition we show that they often obey a surprisingly simple though nontrivial behavior within a model where coexistence is neutrally stable we demonstrate a robust zero one law when the interactions between the three species are generically asymmetric the weakest species survives at a probability that tends to one for large population sizes while the other two are guaranteed to extinction we rationalize our findings from stochastic simulations by an analytic approach

a lattice boltzmann scheme of the navier stokes equation on a three dimensional cuboid lattice abstract the standard lattice boltzmann method lbm for fluid flow simulation is based on a square in 2d or a cubic in 3d lattice grids recently two new lattice boltzmann schemes have been developed on a 2d rectangular grid using the mrt multiple relaxation time collision model either by adding a free parameter in the definition of moments or by extending the equilibrium moments these models satisfy all isotropy conditions and are fully consistent to the navier stokes equations here we developed a lattice boltzmann model on a 3d cuboid lattice namely a lattice grid with different grid lengths in different spatial directions we designed the moment equations derived from our mrt lbm model through the chapman enskog analysis to be fully consistent with the navier stokes equations a second order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities the form of the second order term and the coefficients of the extended equilibrium moments are determined through an inverse design process an additional benefit of the model is that the shear viscosity can be adjusted independent of the stress moment relaxation parameter thus potentially improving the numerical stability of the model the resulting cuboid mrt lbm model is then validated through benchmark simulations using the laminar channel flow the turbulent channel flow and the 3d time dependent energy cascading taylor green vortex flow the second order accuracy of the proposed model is also demonstrated the aspect ratios for numerical stability appear to be constrained at high flow reynolds numbers especially for turbulent flow simulations an aspect requiring further investigation

survival behavior in the cyclic lotka volterra model with a randomly switching reaction rate we study the influence of a randomly switching reproduction predation rate on the survival behavior of the nonspatial cyclic lotka volterra model also known as the zero sum rock paper scissors game used to metaphorically describe the cyclic competition between three species in large and finite populations demographic fluctuations internal noise drive two species to extinction in a finite time while the species with the smallest reproduction predation rate is the most likely to be the surviving one law of the weakest here we model environmental external noise by assuming that the reproduction predation rate of the strongest species the fastest to reproduce and predate in a given static environment randomly switches between two values corresponding to more and less favorable external conditions we study the joint effect of environmental and demographic noise on the species survival probabilities and on the mean extinction time in particular we investigate whether the survival probabilities follow the law of the weakest and analyze their dependence on the external noise intensity and switching rate remarkably when on average there is a finite number of switches prior to extinction the survival probability of the predator of the species whose reaction rate switches typically varies nonmonotonically with the external noise intensity with optimal survival about a critical noise strength we also outline the relationship with the case where all reaction rates switch on markedly different time scales

saddles arrows and spirals deterministic trajectories in cyclic competition of four species population dynamics in systems composed of cyclically competing species has been of increasing interest recently here we investigate a system with four or more species using mean field theory we study in detail the trajectories in configuration space of the population fractions we discover a variety of orbits shaped like saddles spirals and straight lines many of their properties are found explicitly most remarkably we identify a collective variable that evolves simply as an exponential q e t where is a function of the reaction rates it provides information on the state of the system for late times as well as for t we discuss implications of these results for the evolution of a finite stochastic system a generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems

phase transitions and spatio temporal fluctuations in stochastic lattice lotka volterra models we study the general properties of stochastic two species models for predator prey competition and coexistence with lotka volterra type interactions defined on a d dimensional lattice introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical deterministic mean field picture already within mean field theory however spatial constraints modeling locally limited resources lead to the emergence of a continuous active to absorbing state phase transition field theoretic arguments supported by monte carlo simulation results indicate that this transition which represents an extinction threshold for the predator population is governed by the directed percolation universality class in the active state where predators and prey coexist the classical center singularities with associated population cycles are replaced by either nodes or foci in the vicinity of the stable nodes the system is characterized by essentially stationary localized clusters of predators in a sea of prey near the stable foci however the stochastic lattice lotka volterra system displays complex correlated spatio temporal patterns of competing activity fronts correspondingly the population densities in our numerical simulations turn out to oscillate irregularly in time with amplitudes that tend to zero in the thermodynamic limit yet in finite systems these oscillatory fluctuations are quite persistent and their features are determined by the intrinsic interaction rates rather than the initial conditions we emphasize the robustness of this scenario with respect to various model perturbations

when the mean is not enough calculating fixation time distributions in birth death processes studies of fixation dynamics in markov processes predominantly focus on the mean time to absorption this may be inadequate if the distribution is broad and skewed we compute the distribution of fixation times in one step birth death processes with two absorbing states these are expressed in terms of the spectrum of the process and we provide different representations as forward only processes in eigenspace these allow efficient sampling of fixation time distributions as an application we study evolutionary game dynamics where invading mutants can reach fixation or go extinct we also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states whereas the mean fixation time has no such interpretation

modelling dynamics of marathons a mixture model approach abstract in this paper statistical properties of marathon dynamics are studied we find that changes of velocity in marathons follow an unconventional mechanism in which the log change of velocity is highly dependent on current velocity with a complex relationship the conditional distributions of log change of velocity exhibit patterns of varying means variances and skewnesses as such the overall velocity distributions are also found to have departed from gaussian we illustrate the mechanism with a finite mixture of generalized linear regressions with varying weights and skew normal errors and we show that the completion time distribution can be approximated by skewed distributions

coexistence versus extinction in the stochastic cyclic lotka volterra model cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity see e g b kerr m a riley m w feldman and b j m bohannan nature 418 171 2002 and b kirkup and m a riley nature 428 412 2004 through analytical methods supported by numerical simulations we address this issue by studying the properties of a paradigmatic non spatial three species stochastic system namely the rock paper scissors or cyclic lotka volterra model while the deterministic approach rate equations predicts the coexistence of the species resulting in regular yet neutrally stable oscillations of the population densities we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction after long enough time two of the three species die out as main findings we provide analytic estimates and numerical computation of the extinction probability at a given time we also discuss the implications of our results for a broad class of competing population systems

theoretical analysis and simulations of the generalized lotka volterra model the dynamics of generalized lotka volterra systems is studied by theoretical techniques and computer simulations these systems describe the time evolution of the wealth distribution of individuals in a society as well as of the market values of firms in the stock market the individual wealths or market values are given by a set of time dependent variables w i i 1 dots n the equations include a stochastic autocatalytic term representing investments a drift term representing social security payments and a time dependent saturation term due to the finite size of the economy the w i mathrm mathrm s turn out to exhibit a power law distribution of the form p w ensuremath sim w ensuremath 1 ensuremath ensuremath alpha it is shown analytically that the exponent ensuremath alpha can be expressed as a function of one parameter which is the ratio between the constant drift component social security and the fluctuating component investments this result provides a link between the lower and upper cutoffs of this distribution namely between the resources available to the poorest and those available to the richest in a given society the value of ensuremath alpha is found to be insensitive to variations in the saturation term which represent the expansion or contraction of the economy the results are of much relevance to empirical studies that show that the distribution of the individual wealth in different countries during different periods in the 20th century has followed a power law distribution with 1l ensuremath alpha l2

lattice boltzmann method with selective viscosity filter for high reynolds number flows the lattice boltzmann method suffers from numerical instabilities that can induce local blowup of the computation the von neumann stability analysis applied to the lbe bgk and lbe mrt models shows that numerical instabilities occur in the high wavenumber range and are due to the interplay between acoustic modes and some other modes as it is done in the lbe mrt model an increase of the bulk viscosity is an efficient way of damping spurious oscillations however this stabilization method induces an over damping of acoustic waves some selective spatial filters can be used in order to eliminate the spurious small spatial scales without affecting the large scale physical modes three different lattice boltzmann algorithms based on filtering step are proposed the fully filtered lbe the lbe with filtered macroscopic quantities and the lbe with filtered collision operator the behavior of several explicit filter stencils is studied in the fourier space for a given filter stencil the filtered collision operator approach leads to the highest cut off wavenumber in this case the theoretical wavenumber dependent viscosity is n k c s 2 t email protected k 1 2 where f k is the filter shape and s the filter strength under resolved simulations high reynolds number are performed on the case of the doubly periodic shear layers the performance of the three filtered lbe is found to be the same as the mrt model for stability control propagation of acoustic plane waves is also simulated with the three filtering algorithms the measured dissipation of acoustic wave compares well with the theoretical results

effects of time delay on symmetric two species competition subject to noise noise and time delay act simultaneously on real ecological systems the lotka volterra model of symmetric two species competition with noise and time delay was investigated in this paper by means of stochastic simulation we find that i the time delay induces the densities of the two species to periodically oscillate synchronously ii the stationary probability distribution function of the two species densities exhibits a transition from multiple to single stability as the delay time increases iii the characteristic correlation time for the sum of the two species densities squared exhibits a nonmonotonic behavior as a function of delay time our results have the implication that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems

self organized criticality abstract dissipative dynamical systems with many degrees of freedom naturally evolve to a critical state with fluctuations extending over all length and time scales it is suggested and supported by simulations on simple toy model systems that turbulence earthquakes 1 f noise and economics may operate at the self organized critical state

testability of evolutionary game dynamics based on experimental economics data abstract understanding the dynamic processes of a real game system requires an appropriate dynamics model and rigorously testing a dynamics model is nontrivial in our methodological research we develop an approach to testing the validity of game dynamics models that considers the dynamic patterns of angular momentum and speed as measurement variables using rock paper scissors rps games as an example we illustrate the geometric patterns in the experiment data we then derive the related theoretical patterns from a series of typical dynamics models by testing the goodness of fit between the experimental and theoretical patterns we show that the validity of these models can be evaluated quantitatively our approach establishes a link between dynamics models and experimental systems which is to the best of our knowledge the most effective and rigorous strategy for ascertaining the testability of evolutionary game dynamics models

evolutionary dynamics with fluctuating population sizes and strong mutualism game theory ideas provide a useful framework for studying evolutionary dynamics in a well mixed environment this approach however typically enforces a strictly fixed overall population size deemphasizing natural growth processes we study a competitive lotka volterra model with number fluctuations that accounts for natural population growth and encompasses interaction scenarios typical of evolutionary games we show that in an appropriate limit the model describes standard evolutionary games with both genetic drift and overall population size fluctuations however there are also regimes where a varying population size can strongly influence the evolutionary dynamics we focus on the strong mutualism scenario and demonstrate that standard evolutionary game theory fails to describe our simulation results we then analytically and numerically determine fixation probabilities as well as mean fixation times using matched asymptotic expansions taking into account the population size degree of freedom these results elucidate the interplay between population dynamics and evolutionary dynamics in well mixed systems

coevolution of nodes and links diversity driven coexistence in cyclic competition of three species when three species compete cyclically in a well mixed stochastic system of n individuals extinction is known to typically occur at times scaling as the system size n this happens for example in rock paper scissors games or conserved lotka volterra models in which every pair of individuals can interact on a complete graph here we show that if the competing individuals also have a social temperament to be either introverted or extroverted leading them to cut or add links respectively then long living states in which all species coexist can occur these nonequilibrium quasisteady states only occur when both introverts and extroverts are present thus showing that diversity can lead to stability in complex systems in this case it enables a subtle balance between species competition and network dynamics to be maintained

scaling properties of marathon races abstract some regularities in popular marathon races are identified in this paper it is found for high performance participants i e racing times in the range 2 15 3 15 h the average velocity as a function of the marathoner s ranking behaves as a power law which may be suggesting the presence of critical phenomena elite marathoners with racing times below 2 15 h can be considered as outliers with respect to this behavior for the main marathon pack i e racing times in the range 3 00 6 00 h the average velocity as a function of the marathoner s ranking behaves linearly for this racing times the interpersonal velocity defined as the difference of velocities between consecutive runners displays a continuum of scaling behavior ranging from uncorrelated noise for small scales to correlated 1 f noise for large scales it is a matter of fact that 1 f noise is characterized by correlations extended over a wide range of scales a clear indication of some sort of cooperative effect

invasion controlled pattern formation in a generalized multispecies predator prey system rock scissors paper game as the simplest model of intransitive relation between competing agents is a frequently quoted model to explain the stable diversity of competitors in the race of surviving when increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator prey like dominance a balanced or peer relation can emerge between some competitors by utilizing this possibility in the present work we generalize a four state predator prey type model where we establish two groups of species labeled by even and odd numbers in particular we introduce different invasion probabilities between and within these groups which results in a tunable intensity of bidirectional invasion among peer species our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion the related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay on the fraction of empty sites and on the variance of the species density furthermore the application of diverse alliance specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate these observations highlight that beyond the well known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier

tests for conditional ellipticity in multivariate garch models tests are proposed for the assumption that the conditional distribution of a multivariate garch process is elliptic these tests are of kolmogorov smirnov and cramer von mises type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution the asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions it is shown that both the finite sample and the asymptotic null distribution depend on the unknown distribution of the euclidean norm of the innovations therefore a conditional monte carlo procedure is used to actually carry out the tests the validity of this resampling scheme is formally justified results on the behavior of the new tests in finite samples are included along with comparisons with other tests

rock scissors paper game on regular small world networks the spatial rock scissors paper game or cyclic lotka volterra system is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours degree at each site on the square lattice this system exhibits a self organizing pattern with equal concentration of the competing strategies species if the quenched background is constructed by substituting random links for the nearest neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value this transition can also be observed if the standard link is replaced temporarily by a random one with a probability p at each step of iteration above a second threshold value of p the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous absorbing states in this case the results of monte carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one two four and six site clusters

inferential aspects of the skew exponential power distribution when the analysis of real data indicates that normality assumptions are untenable more flexible models that cope with the most prevalent deviations from normality can be adopted in this context the skew exponential power sep distribution warrants special attention because it encompasses distributions having both heavy tails and skewness it allows likelihood inference and it includes the normal model as a special case this article concerns likelihood inference about the parameters of the sep family in particular the information matrix of the maximum likelihood estimators mles is obtained and finite sample properties of the estimators are investigated numerically special attention is given to the properties of the mles and likelihood ratio statistics when the data are drawn from a normal distribution because this case is relevant for using the sep distribution to test for normality application of the sep distribution in robust estimation problems is considered for both independent and depend

stability hopf bifurcations and spatial patterns in a delayed diffusive predator prey model with herd behavior in this paper we consider a delayed diffusive predator prey model with herd behavior firstly by choosing the appropriate bifurcation parameter the stability of the positive equilibria and the existence of hopf bifurcations induced by diffusion and delay respectively are investigated by analyzing the corresponding characteristic equation then applying the normal form theory and the center manifold argument for partial functional differential equations the formula determining the properties of the hopf bifurcation are obtained furthermore the instability of the hopf bifurcation leads to the emergence of spatial patterns finally some numerical simulations are also carried out to illustrate and expand the theoretical results

vortices and strings in a model ecosystem we study the spatial pattern formation in a model ecosystem by the position fixed reaction method this ecosystem contains three biospecies whose competing powers are cyclic it is well known that this system is self organized into a quasistationary state and that the mean field approximation mfa never predicts such a pattern formation recently several authors applied the pair approximation pa and obtained considerable improvements however applying pa to our ecosystem fails to yield such an improvement as revealed by computer simulations the failures of mfa and pa may be attributed to the fact that both approximations neglect a long range correlation thus we introduce the concept of topological defects such as vortices or strings and demonstrate that the dynamics of these defects can at least qualitatively account for the observed pattern formation dynamics

coexistence and survival in conservative lotka volterra networks analyzing coexistence and survival scenarios of lotka volterra lv networks in which the total biomass is conserved is of vital importance for the characterization of long term dynamics of ecological communities here we introduce a classification scheme for coexistence scenarios in these conservative lv models and quantify the extinction process by employing the pfaffian of the network s interaction matrix we illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

modeling and inference with υ spherical distributions abstract a new class of continuous multivariate distributions on n is proposed we define these so called spherical distributions through properties of the density function in a location scale context we derive conditions for properness of spherical distributions and discuss how to generate them in practice the name spherical is motivated by the fact that these distributions generalize the classes of spherical when is the l 2 norm and l q spherical when is the l q norm distributions isodensity sets are still always situated around the location parameter but exchangeability and axial symmetry are no longer imposed as is illustrated in some examples as an important special case we define a class of distributions suggested by independent sampling from a generalization of exponential power distributions this allows us to model skewness interestingly all the robustness results found previously for spherical and l q spherical models carry over directly to spherical mo

predominance of the weakest species in lotka volterra and may leonard formulations of the rock paper scissors model we revisit the problem of the predominance of the weakest species in the context of lotka volterra and may leonard formulations of a spatial stochastic rock paper scissors model in which one of the species has its predation probability reduced by 0l mathcal p w l1 we show that despite the different population dynamics and spatial patterns these two formulations lead to qualitatively similar results for the late time values of the relative abundances of the three species as a function of mathcal p w as long as the simulation lattices are sufficiently large for coexistence to prevail the weakest species generally having an advantage over the others specially over its predator however for smaller simulation lattices we find that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size

properties and estimation of asymmetric exponential power distribution the new distribution class asymmetric exponential power distribution aepd proposed in this paper generalizes the class of skewed exponential power distributions sepd in a way that in addition to skewness introduces different decay rates of density in the left and right tails our parametrization provides an interpretable role for each parameter we derive moments and moment based measures skewness kurtosis expected shortfall it is demonstrated that a maximum entropy property holds for the aepd distributions we establish consistency asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix where the results apply to the sepd class they enlarge on the current literature also we give a convenient stochastic representation of the distribution our monte carlo study illustrates the theoretical results we also provide some empirical evidence for the usefulness of employing aepd errors in garch type models for predicting downside market risk of financial assets

lattice boltzmann method on curvilinear coordinates system using an interpolation based strategy the lattice boltzmann method is extended to apply to general curvilinear coordinate systems as an example a cylindrical coordinate system is used to simulate two dimensional flow around a circular cylinder numerical simulations are carried out for impulsive initial conditions with reynolds numbers up to 104 the agreement of our results with previous computational and experimental results is satisfactory compared with previous lattice boltzmann simulations of the same problem our new approach greatly enhances the computational efficiency

spirals and coarsening patterns in the competition of many species a complex ginzburg landau approach in order to model real ecological systems one has to consider many species that interact in complex ways however most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions the few studies dealing with larger number of species and or more complex interaction schemes are mostly restricted to numerical explorations in this paper we determine starting from the deterministic mean field rate equations for large classes of systems the space of coexistence fixed points at which biodiversity is maximal for systems with a single coexistence fixed point we derive complex ginzburg landau equations that allow to describe space time pattern realized in two space dimensions for selected cases we compare the theoretical predictions with the pattern observed in numerical simulations

separation of cyclic and starlike hierarchical dominance in evolutionary matrix games we study antisymmetric components of matrices characterizing pair interactions in multistrategy evolutionary games based on the dyadic decomposition of matrices we distinguish cyclic and starlike hierarchical dominance in the appropriate components in the symmetric matrix games the strengths of these elementary components are determined the general features and intrinsic symmetries of these interactions are represented by directed graphs it is found that the variation of a single matrix component modifies simultaneously the strengths of two starlike hierarchical basis games and many other independent rock paper scissors type cyclic basis games the application of the related concepts is illustrated by discussing the three strategy voluntary prisoner s dilemma

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

evolutionary game theory theoretical concepts and applications to microbial communities ecological systems are complex assemblies of large numbers of individuals interacting competitively under multifaceted environmental conditions recent studies using microbial laboratory communities have revealed some of the self organization principles underneath the complexity of these systems a major role of the inherent stochasticity of its dynamics and the spatial segregation of different interacting species into distinct patterns has thereby been established it ensures the viability of microbial colonies by allowing for species diversity cooperative behavior and other kinds of social behavior a synthesis of evolutionary game theory nonlinear dynamics and the theory of stochastic processes provides the mathematical tools and a conceptual framework for a deeper understanding of these ecological systems we give an introduction into the modern formulation of these theories and illustrate their effectiveness focussing on selected examples of microbial systems intrinsic fluctuations stemming from the discreteness of individuals are ubiquitous and can have an important impact on the stability of ecosystems in the absence of speciation extinction of species is unavoidable it may however take very long times we provide a general concept for defining survival and extinction on ecological time scales spatial degrees of freedom come with a certain mobility of individuals when the latter is sufficiently high bacterial community structures can be understood through mapping individual based models in a continuum approach onto stochastic partial differential equations these allow progress using methods of nonlinear dynamics such as bifurcation analysis and invariant manifolds we conclude with a perspective on the current challenges in quantifying bacterial pattern formation and how this might have an impact on fundamental research in non equilibrium physics

some progress in lattice boltzmann method part i nonuniform mesh grids a new lattice boltzmann algorithm is proposed to simulate the navier stokes equation on arbitrary nonuniform mesh grids the new algorithm retains the advantages of the lattice boltzmann method parallel of algorithm ease of programming and ability to incorporate microscopic interactions a simulation of flow in a two dimensional symmetric channel with sudden expansion is carried out using the new algorithm on a nonuniform mesh the results of the simulation are in excellent agreement with previous experimental and numerical results

interplay between partnership formation and competition in generalized may leonard games in order to better understand the interplay of partnership and competition in population dynamics we study a family of generalized may leonard models with n species these models have a very rich structure characterized by different types of space time patterns interesting partnership formations emerge following the maxim that the enemy of my enemy is my friend in specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation we classify the different types of dynamics through the analysis of the square of the adjacency matrix the dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a fourier analysis finally after having identified collaborating teams we study interface fluctuations where we initially populate different parts of the system with different teams

detrended fluctuation analysis of time series of a firing fusimotor neuron abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk model analysis thus we have found evidence for the white noise characteristics of the isi time series which means that the fusimotor activity does not possess temporal correlations we conclude that such an activity represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles

coevolutionary dynamics from finite to infinite populations traditionally frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations however the relationship between deterministic and stochastic approaches remained unclear here we solve this problem by explicitly considering large populations in particular we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics moreover differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and depending on the population size can even invert the direction of the evolutionary process

derivation of the lattice boltzmann method by means of the discrete ordinate method for the boltzmann equation in this note we show that the lattice boltzmann bgk method in common use can be derived from the boltzmann equation itself according to the present derivation it is apparent that the equation thus derived can be reduced to the navier stokes equation at a limit of small knudsen number since the equation thus derived is the boltzmann equation itself hence the present derivation method gives us a simple and flexible recipe to construct the lattice boltzmann method and makes it easy to construct an extended lattice boltzmann method in various ways 15 refs 1 fig

three and four state rock paper scissors games with diffusion cyclic dominance of three species is a commonly occurring interaction dynamics often denoted the rock paper scissors rps game such a type of interactions is known to promote species coexistence here we generalize recent results of reichenbach et al nature london 448 1046 2007 of a four state variant of the rps game we show that spiral formation takes place only without a conservation law for the total density nevertheless in general fast diffusion can destroy species coexistence we also generalize the four state model to slightly varying reaction rates this is shown both analytically and numerically not to change pattern formation or the effective wavelength of the spirals and therefore not to alter the qualitative properties of the crossover to extinction

football goal distributions and extremal statistics we analyse the distributions of the number of goals scored by home teams away teams and the total scored in the match in domestic football games from 169 countries between 1999 and 2001 the probability density functions pdfs of goals scored are too heavy tailed to be fitted over their entire ranges by poisson or negative binomial distributions which would be expected for uncorrelated processes log normal distributions cannot include zero scores and here we find that the pdfs are consistent with those arising from extremal statistics in addition we show that it is sufficient to model english top division and fa cup matches in the seasons of 1970 71 2000 01 on poisson or negative binomial distributions as reported in analyses of earlier seasons and that these are not consistent with extremal statistics

nonexistence of h theorems for the athermal lattice boltzmann models with polynomial equilibria we prove that no h theorem exists for the athermal lattice boltzmann equation with polynomial equilibria satisfying the conservation laws exactly and explicitly the proof is demonstrated by using the seven velocity model in a triangular lattice in two dimensions and can be readily extended to other lattice boltzmann models in two and three dimensions some issues pertinent to the numerical instabilities of the lattice boltzmann method are disscussed

pattern dynamics of a spatial epidemic model with time delay we presented an epidemic model with delay emergence of spatial pattern is obtained rich dynamics is shown by analysis and numerical results observed data confirms our theoretical results the nonlinear incidence rate can explain the complicated infectious process of disease and time delay describing the latent period widely exists in the process of disease contagion in this paper a spatiotemporal epidemic model with nonlinear incidence rate is investigated in particular we considered that the time delay is relatively small in this case the characteristic equation are derived we obtain two mechanisms of instability of the positive constant stationary state that is one is the diffusion induced instability and the other one is delay induced instability moreover the results of numerical simulation validate our theoretical analyses the obtained results may well catch some major features for epidemic models

coevolutionary dynamics in large but finite populations coevolving and competing species or game theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking recently an explicit mean field description in the form of a fokker planck equation was derived for frequency dependent selection with two strategies in finite populations based on microscopic processes a traulsen j c claussen and c hauert phys rev lett 95 238701 2005 here we generalize this approach in a twofold way first we extend the framework to an arbitrary number of strategies and second we allow for mutations in the evolutionary process the deterministic limit of infinite population size of the frequency dependent moran process yields the adjusted replicator mutator equation which describes the combined effect of selection and mutation for finite populations we provide an extension taking random drift into account in the limit of neutral selection i e whenever the process is determined by random drift and mutations the stationary strategy distribution is derived this distribution forms the background for the coevolutionary process in particular a critical mutation rate uc is obtained separating two scenarios above uc the population predominantly consists of a mixture of strategies whereas below uc the population tends to be in homogeneous states for one of the fundamental problems in evolutionary biology the evolution of cooperation under darwinian selection we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes this approach complements simulation results and provides a deeper systematic understanding of coevolutionary dynamics

topologically robust zero sum games and pfaffian orientation how network topology determines the long time dynamics of the antisymmetric lotka volterra equation to explore how the topology of interaction networks determines the robustness of dynamical systems we study the antisymmetric lotka volterra equation alve the alve is the replicator equation of zero sum games in evolutionary game theory in which the strengths of pairwise interactions between strategies are defined by an antisymmetric matrix such that typically some strategies go extinct over time here we show that there also exist topologically robust zero sum games such as the rock paper scissors game for which all strategies coexist for all choices of interaction strengths we refer to such zero sum games as coexistence networks and construct coexistence networks with an arbitrary number of strategies by mapping the long time dynamics of the alve to the algebra of antisymmetric matrices we identify simple graph theoretical rules by which coexistence networks are constructed examples are triangulations of cycles characterized by the golden ratio phi 1 6180 cycles with complete subnetworks and non hamiltonian networks in graph theoretical terms we extend the concept of a pfaffian orientation from even sized to odd sized networks our results show that the topology of interaction networks alone can determine the long time behavior of nonlinear dynamical systems and may help to identify robust network motifs arising for example in ecology

on the finite difference based lattice boltzmann method in curvilinear coordinates the lattice boltzmann method is a microscopic based approach for solving the fluid flow problems at the macroscopic scales the presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility to circumvent such difficulties a finite difference based lattice boltzmann method fdlbm in curvilinear coordinates is explored using body fitted coordinates with non uniform grids several test cases including the impulsively started cylindrical couette flow steady state cylindrical couette flow steady flow over flat plates and steady flow over a circular cylinder are used to examine various issues related to the fdlbm the effect of boundary conditions for the distribution functions on the solution the merits between second order central difference and upwind schemes for advection terms and the effect of the reynolds number are investigated favorable results are obtained using fdlbm in curvilinear coordinates indicating that the method is potentially capable of solving finite reynolds number flow problems in complex geometries

cycle frequency in standard rock paper scissors games evidence from experimental economics the rock paper scissors rps game is a widely used model system in game theory evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the rps game but experimental evidence has remained to be rather weak in this work we performed laboratory experiments on the rps game and analyzed the social state evolutionary trajectories of twelve populations of n 6 players we found strong evidence supporting the existence of persistent cycles the mean cycling frequency was measured to be 0 029 0 009 period per experimental round our experimental observations can be quantitatively explained by a simple non equilibrium model namely the discrete time logit dynamical process with a noise parameter our work therefore favors the evolutionary game theory over the classical game theory for describing the dynamical behavior of the rps game c 2013 the authors published by elsevier b v all rights reserved

diversity in interaction strength promotes rich dynamical behaviours in a three species ecological system abstract asymmetrical interactions are thought to have an important influence on multi species competitive systems and understanding this ecological process is a challenging task because of uncertain roles that asymmetrical interactions can have in maintaining species biodiversity to address this problem we employ a simple ecological model for multiple species with asymmetrical competitive strength and we analyse this model using the techniques from dynamical systems and bifurcation analysis in particular we examine the stability properties of steady states and also its bifurcation structures under parameter variation we demonstrate that there exists threshold values for asymmetrical competitive strength which correspond to transcritical and supercritical hopf bifurcations the occurrence of these bifurcations give rise to numerous dynamics in the model e g multi species coexistence species exclusion alternative stable state communities and oscillatory dynamics among multiple species additionally we observe the conditions under which co dimension two gavrilov guckenheimer bifurcation occurs as a result of the interaction between transcritical and hopf bifurcations which can lead to complex dynamics we also investigate how diversity in interaction strength between multiple competing species causes counterintuitive observations on one hand asymmetrical interactions promote the maintenance of biodiversity through multi species coexistence state and also coexistence via stable limit cycles corresponding to oscillatory dynamics on the other hand we also observe that the occurrence of stable limit cycles can lead to destabilisation of multi species communities

two dimensional lattice boltzmann model for compressible flows with high mach number abstract in this paper we present an improved lattice boltzmann model for compressible navier stokes system with high mach number the model is composed of three components i the discrete velocity model by m watari and m tsutahara phys rev e 67 2003 036306 ii a modified lax wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included iii artificial viscosity the improved model is convenient to compromise the high accuracy and stability the included dispersion term can effectively reduce the numerical oscillation at discontinuity the added artificial viscosity helps the scheme to satisfy the von neumann stability condition shock tubes and shock reflections are used to validate the new scheme in our numerical tests the mach numbers are successfully increased up to 20 or higher the flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems

fluctuations and correlations in lattice models for predator prey interaction including spatial structure and stochastic noise invalidates the classical lotka volterra picture of stable regular population cycles emerging in models for predator prey interactions growth limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class we discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator prey model variant where the predation process includes next nearest neighbor interactions we find that the corresponding stochastic model reproduces the above scenario in dimensions 1 d or 4 in contrast with the mean field theory which predicts a first order phase transition however the mean field features are recovered upon allowing for nearest neighbor particle exchange processes provided these are sufficiently fast

fixation in a cyclic lotka volterra model we study a cyclic lotka volterra model of n interacting species populating a d dimensional lattice in the realm of a kirkwood approximation a critical number of species nc d above which the system fixates is determined analytically we find nc d 5 14 23 in dimensionsdd 1 2 3 in remarkably good agreement with simulation results in two dimensions a cyclic variant of the lotka volterra model of interacting populations originally introduced by vito volterra for the description of the struggle for existence among species 1 2 has then appeared in a number of apparently unrelated fields ranging from plasma physics 3 to integrable systems 4 5 recently the cyclic lotka volterra model also known as the cyclic voter model has attracted considerable interest as it was realized that introduction of the spatial structure drastically enriches the dynamics 6 11 namely if species live on a one dimensional 1d lattice a homogeneous initial state evolves into a coarsening mosaic of interacting species this heterogeneous spatial structure spontaneously develops when the number of species is sufficiently small n nc fixation occurs i e the system approaches a frozen state little is known in higher dimensions not even the existence of nc has yet been established theoretically or numerically in simulations on two dimensional 2d lattices with n 6 10 species no sign of fixation has been found and instead a reactive steady state has been observed 6 11 in this letter we investigate the cyclic lotka volterra model in the framework of a kirkwood like approximation this approach predicts a finite nc in all spatial dimensions in the following we shall use the language of the voter model 12 consider the cyclic voter model with n possible opinions each site of a d dimensional cubic lattice is occupied by a voter which has an opinion labelled by with d 1 n voters can change their opinions in a cyclic manner 1 modulo n according to the opinions of their neighbourhood specifically the following sequential dynamics is implemented i we randomly choose a site of opinion say and one of its 2d nearest neighbours of opinion ii if d 1 then the chosen site changes its opinion from to d 1 and iii otherwise opinion does not change we set the timescale so that in unit time each site of the lattice is chosen once on average when nd 2 the cyclic voter model is

investigation of stability and hydrodynamics of different lattice boltzmann models stability and hydrodynamic behaviors of different lattice boltzmann models including the lattice boltzmann equation lbe the differential lattice boltzmann equation dlbe the interpolation supplemented lattice boltzmann method islbm and the taylor series expansion and least square based lattice boltzmann method tllbm are studied in detail our work is based on the von neumann linearized stability analysis under a uniform flow condition the local stability and hydrodynamic dissipation behaviors are studied by solving the evolution operator of the linearized lattice boltzmann equations numerically our investigation shows that the lbe schemes with interpolations such as dlbe islbm and tllbm improve the numerical stability by increasing hyper viscosities at large wave numbers small scales it was found that these interpolated lbe schemes with the upwind interpolations are more stable than those with central interpolations because of much larger hyper viscosities

synchronization and extinction in cyclic games with mixed strategies we consider cyclic lotka volterra models with three and four strategies where at every interaction agents play a strategy using a time dependent probability distribution agents learn from a loss by reducing the probability to play a losing strategy at the next interaction for that an agent is described as an urn containing balls of three and four types respectively where after a loss one of the balls corresponding to the losing strategy is replaced by a ball representing the winning strategy using both mean field rate equations and numerical simulations we investigate a range of quantities that allows us to characterize the properties of these cyclic models with time dependent probability distributions for the three strategy case in a spatial setting we observe a transition from neutrally stable to stable when changing the level of discretization of the probability distribution for large values of yielding a good approximation to a continuous distribution spatially synchronized temporal oscillations dominate the system for the four strategy game the system is always neutrally stable but different regimes emerge depending on the size of the system and the level of discretization

extinction in neutrally stable stochastic lotka volterra models populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions the processes leading to extinction of species whose understanding is a key component in the study of evolution and biodiversity are influenced by both of these factors here we investigate a class of stochastic population dynamics models based on generalized lotka volterra systems in the case of neutral stability of the underlying deterministic model the impact of intrinsic noise on the survival of species is dramatic it destroys coexistence of interacting species on a time scale proportional to the population size we introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower dimensional effective dynamics this is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations the extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations

lattice boltzmann computational fluid dynamics in three dimensions the recent development of the lattice gas method and its extension to the lattice boltzmann method have provided new computational schemes for fluid dynamics both methods are fully paralleled and can easily model many different physical problems including flows with complicated boundary conditions in this paper basic principles of a lattice boltzmann computational method are described and applied to several three dimensional benchmark problems in most previous lattice gas and lattice boltzmann methods a face centered hyper cubic lattice in four dimensional space was used to obtain an isotropic stress tensor to conserve computer memory we develop a model which requires 14 moving directions instead of the usual 24 directions lattice boltzmann models describing two phase fluid flows and magnetohydrodynamics can be developed based on this simpler 14 directional lattice comparisons between three dimensional spectral code results and results using our method are given for simple periodic geometries an important property of the lattice boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency while all other methods including the spectral method are unable to model complicated geometries efficiently

characterization of spiraling patterns in spatial rock paper scissors games the spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research here we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions inspired by recent experiments we consider a generic metapopulation model comprising rock paper scissors interactions via dominance removal and replacement reproduction mutations pair exchange and hopping of individuals by combining analytical and numerical methods we obtain the model s phase diagram near its hopf bifurcation and quantitatively characterize the properties of the spiraling patterns arising in each phase the phases characterizing the cyclic competition away from the hopf bifurcation at low mutation rate are also investigated our analytical approach relies on the careful analysis of the properties of the complex ginzburg landau equation derived through a controlled perturbative multiscale expansion around the model s hopf bifurcation our results allow us to clarify when spatial rock paper scissors competition leads to stable spiral waves and under which circumstances they are influenced by nonlinear mobility

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends