refined composite multivariate generalized multiscale fuzzy entropy a tool for complexity analysis of multichannel signals abstract multiscale entropy mse is an appealing tool to characterize the complexity of time series over multiple temporal scales recent developments in the field have tried to extend the mse technique in different ways building on these trends we propose the so called refined composite multivariate multiscale fuzzy entropy rcmvmfe whose coarse graining step uses variance rcmvmfe 2 or mean rcmvmfe we investigate the behavior of these multivariate methods on multichannel white gaussian and 1 f noise signals and two publicly available biomedical recordings our simulations demonstrate that rcmvmfe 2 and rcmvmfe lead to more stable results and are less sensitive to the signals length in comparison with the other existing multivariate multiscale entropy based methods the classification results also show that using both the variance and mean in the coarse graining step offers complexity profiles with complementary information for biomedical signal analysis we also made freely available all the matlab codes used in this paper

statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

emd based refined composite multiscale entropy analysis of complex signals abstract multiscale entropy mse is an effective method to measure the complexity of signals from complex systems which has been applied to various fields successfully however mse may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse graining procedure reduces the length of data considerably at large scales refined composite multiscale entropy rcmse is then developed to solve this problem however trends superimposed in signals may significantly affect the complexity measurement thus we introduce an empirical mode decomposition based rcmse called emd rcmse to first eliminate such effects of trends and then measure the complexity of signals it is validated from simulated signals and has good estimation in addition this method is also applied to study the complexity of traffic signals and we obtain some interesting results 1 traffic signals are more complex than the results showing from rcmse mse 2 weekday and weekend patterns different combination of trends greatly affect the results 3 complexity indices change with time at each day due to the degree of human activities

rank driven markov processes we study a class of markovian systems of n elements taking values in 0 1 that evolve in discrete time t via randomized replacement rules based on the ranks of the elements these rank driven processes are inspired by variants of the bak sneppen model of evolution in which the system represents an evolutionary fitness landscape and which is famous as a simple model displaying self organized criticality our main results are concerned with long time large n asymptotics for the general model in which at each time step k randomly chosen elements are discarded and replaced by independent u 0 1 variables where the ranks of the elements to be replaced are chosen independently at each time step according to a distribution n on 1 2 n k our main results are that under appropriate conditions on n the system exhibits threshold behavior at s 0 1 where s is a function of n and the marginal distribution of a randomly selected element converges to u s 1 as t and n of this class of models results in the literature have previously been given for special cases only namely the mean field or random neighbor bak sneppen model our proofs avoid the heuristic arguments of some of the previous work and use foster lyapunov ideas our results extend existing results and establish their natural more general context we derive some more specialized results for the particular case where k 2 one of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic markov chains on increasing state spaces which may be of independent interest

variational reduction for ginzburg landau vortices let be a bounded domain with smooth boundary in r2 we construct non constant solutions to the complex valued ginzburg landau equation e2 u 1 u 2 u 0 in as e 0 both under zero neumann and dirichlet boundary conditions we reduce the problem of finding solutions having isolated zeros vortices with degrees 1 to that of finding critical points of a small c1 perturbation of the associated renormalized energy this reduction yields general existence results for vortex solutions in particular for the neumann problem we find that if is not simply connected then for any k 1 a solution with exactly k vortices of degree one exists

refined generalized multiscale entropy analysis for physiological signals abstract multiscale entropy analysis has become a prevalent complexity measurement and been successfully applied in various fields however it only takes into account the information of mean values first moment in coarse graining procedure then generalized multiscale entropy mse n considering higher moments to coarse grain a time series was proposed and mse 2 has been implemented however the mse 2 sometimes may yield an imprecise estimation of entropy or undefined entropy and reduce statistical reliability of sample entropy estimation as scale factor increases for this purpose we developed the refined model rmse 2 to improve mse 2 simulations on both white noise and 1 f noise show that rmse 2 provides higher entropy reliability and reduces the occurrence of undefined entropy especially suitable for short time series besides we discuss the effect on rmse 2 analysis from outliers data loss and other concepts in signal processing we apply the proposed model to evaluate the complexity of heartbeat interval time series derived from healthy young and elderly subjects patients with congestive heart failure and patients with atrial fibrillation respectively compared to several popular complexity metrics the results demonstrate that rmse 2 measured complexity a decreases with aging and diseases and b gives significant discrimination between different physiological pathological states which may facilitate clinical application

on the phase space approach to complexity we elaborate in some detail on a new phase space approach to complexity due to y c zhang we show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle for a 1d signal we find 1 f noise in accordance with zhang

cumulative tsallis entropy based on multi scale permuted distribution of financial time series abstract a method based on multi scale permuted distribution cumulative tsallis entropy mpdcte is proposed in this paper to measure the complexity and dissimilarity between sequences it avoids the influence of permutation on spatial distribution and uses the calculation of spatial distance matrix in distributed entropy to effectively measure the complexity of time series we apply the mpdcte method to the simulation data verify the effectiveness of the method discuss the influence of the parameters and compare it with the traditional entropy metric the results show that this method is insensitive to parameter changes and has a low dependence on data length the dependencies all show superiority finally it was applied to the real financial market and we selected 9 stocks in the world to analyze the mpdcte method clearly divided the stocks by analyzing the sequence which is consistent with the phenomenon of the financial market

existence of at least three solutions of a second order three point boundary value problem abstract we study existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type x f t x x t i 0 1 x 0 0 x 1 x 0 1 0 1 the growth of f with respect to x is allowed to be quadratic we use some degree theory arguments to get the multiplicity result

the screening of species in a darwinistic tree like model of evolution abstract numerical and theoretical investigations of a tree like model of self organized critical evolution are presented the screening of species from the evolution process is numerically studied critical exponents for i the avalanche distribution ii the correlation function iii the order parameter and iv the fraction of unscreened species are given a mean field approximation is developed this theory is quite accurate for describing the critical state but is not able to describe the transient regimes i e the self organized slowing down of both order parameter and fraction of unscreened species towards the critical state

non triviality of a discrete bak sneppen evolution model consider the following evolution model proposed in ref 1 by bak and sneppen put n vertices on a circle spaced evenly each vertex represents a certain species we associate with each vertex a random variable representing the state or fitness of the species with values in 0 1 the dynamics proceeds as follows every discrete time step we choose the vertex with minimal fitness and assign to this vertex and to its two neighbours three new independent fitnesses with a uniform distribution on 0 1 a conjecture of physicists based on simulations is that in the stationary regime the one dimensional marginal distributions of the fitnesses converges when n to a uniform distribution on f 1 for some threshold f 1 in this paper we consider a discrete version of this model proposed in ref 2 in this discrete version the fitness of a vertex can be either 0 or 1 the system evolves according to the following rules each discrete time step we choose an arbitrary vertex with fitness 0 if all the vertices have fitness 1 then we choose an arbitrary vertex with fitness 1 then we update the fitnesses of this vertex and of its two neighbours by three new independent fitnesses taking value 0 with probability 0 q 1 and 1 with probability p 1 q we show that if q is close enough to one then the mean average fitness in the stationary regime is bounded away from 1 uniformly in the number of vertices this is a small step in the direction of the conjecture mentioned above and also settles a conjecture mentioned in ref 2 our proof is based on a reduction to a continuous time particle system

vortices in complex scalar fields abstract consider a spatially extended field which evolves in time according to a pde the solutions contain particle like defects whose motions are parts of the full dynamics we inquire into the formulation of an asymptotic particle field defect dynamics which derives from the full pde we carry out this program for two complex scalar field equations in two space dimensions the nonlinear schrodinger equation and the nonlinear heat equation the topological defects are zeros of the complex scalar field with nonzero integer winding numbers called vortices vortices evolving under the nonlinear schrodinger equation behave like point vortices in ideal fluid pairs of vortices evolving under the nonlinear heat equation with like opposite winding numbers undergo a repulsive attractive interaction

numerical study of quantized vortex interaction in complex ginzburg landau equation on bounded domains in this paper we study numerically quantized vortex dynamics and their interaction in the two dimensional complex ginzburg landau equation cgle with a dimensionless parameter e 0 on bounded domains under either dirichlet or homogeneous neumann boundary condition we begin with a review of the reduced dynamical laws rdls for time evolution of quantized vortex centers in cgle and show how to solve these nonlinear ordinary differential equations numerically then we present efficient and accurate numerical methods for solving the cgle on either a rectangular or a disk domain under either dirichlet or homogeneous neumann boundary condition based on these efficient and accurate numerical methods for cgle and the rdls we explore rich and complicated quantized vortex dynamics and interaction of cgle with different e and under different initial physical setups including single vortex vortex pair vortex dipole and vortex lattice compare them with those obtained from the corresponding rdls and identify the cases where the rdls agree qualitatively and or quantitatively as well as fail to agree with those from cgle on vortex interaction finally we also obtain numerically different patterns of the steady states for quantized vortex lattices in the cgle dynamics on bounded domains

the origin of power law distributions in self organized criticality the origin of power law distributions in self organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process an avalanche is then regarded as a first return random walk process in a one dimensional lattice power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions this shows that power law distributions in self organized criticality may be caused by the balance of competitive interactions at the mean time the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime

a generalized upper and lower solutions method and multiplicity results for nonlinear first order ordinary differential equations abstract we introduce a generalized upper and lower solutions method for the solvability of first order ordinary differential equations u t t u t u 0 u 1 in order to cover the case when the function satisfies caratheodory conditions this method is then applied to get multiplicity results when the nonlinearity interacts with the real eigenvalue of the linearized problem our proofs are based on differential inequalities and classical leray schauder degree

probabilistic approach to the bak sneppen model we study here the bak sneppen model a prototype model for the study of self organized criticality in this model several species interact and undergo extinction with a power law distribution of activity bursts species are defined through their fitness whose distribution in the system is uniform above a certain threshold run time statistics is introduced for the analysis of the dynamics in order to explain the peculiar properties of the model this approach based on conditional probability theory takes into account the correlations due to memory effects in this way we may compute analytically the value of the fitness threshold with the desired precision this represents a substantial improvement with respect to the traditional mean field approach

on a local version of the bak sneppen model a major difficulty in studying the bak sneppen model is in effectively comparing it with well understood models this stems from the use of two geometries complete graph geometry to locate the global fitness minimizer and graph geometry to replace the species in the neighborhood of the minimizer over the years a number of models inspired by bak sneppen were studied usually by introducing different or new features e g discretizing fitness randomized neighbors or population size we present a variant that only uses features present in bak sneppen and whose difference from the bak sneppen is that only the graph geometry is used for the evolution this allows to obtain the stationary distribution through random walk dynamics while preserving the geometric nature of the model we use this to show that for constant degree graphs the stationary fitness distribution converges to an iid law as the number of vertices tends to infinity we also discuss exponential ergodicity through coupling and avalanches for the model

a unified approach to some two point three point and four point boundary value problems with caratheodory functions this paper deals with boundary value problems formula and formula wherea b 0 0 aandbare given real numbers gis a continuous strictly increasing function withg r r andfis a caratheodory function satisfying a nagumo condition the problems have solutions if and only if there exist a lower solutionxand an upper solutionyandx t y t for alla t b

mixed vortex antivortex solutions of ginzburg landau equations suppose that v e 0 is a family of minimizers of 1 2 then there is a positive number eo g ft such that for any 0 e0 v has precisely idl isolated zeros inside f all of degree sign d where d deg g 0 is the degree of the map g 0ft n 1 see bbh bcp when ft is star shaped the general case relies on an estimate of stl moreover for any sequence of end0 there is a subsequence of v which converges to a map v x of the form

extremal dynamics on complex networks analytic solutions the bak sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks by using the rate equation and the random walk approaches we obtain the analytic solution of the fitness threshold x c to be 1 k f 1 where k f k 2 k k in the quenched annealed updating case where k n is the n text th moment of the degree distribution thus the threshold is zero finite for the degree exponent ensuremath gamma l3 ensuremath gamma g3 for the quenched case in the thermodynamic limit the theoretical value x c fits well to the numerical simulation data in the annealed case only avalanche size defined as the duration of successive mutations below the threshold exhibits a critical behavior as its distribution follows a power law p a s ensuremath sim s ensuremath 3 2

chaotic dynamics markovian coarse graining and information abstract the conditions for mapping chaotic dynamics into a markov chain through finite coarse graining are derived a chapman kolmmogorov equation giving rise to an h theorem is deduced in which the transition probability matrix is expressed entirely in terms of the properties of the underlying deterministic dynamics and of the phase space partition the validity of the conditions ensuring the mapping is verified on simple models of dissipative as well as conservative dynamical systems the implications of the results in the problem of irreversibility and the relation between deterministic chaos information and complexity are discussed

modified multiscale entropy for short term time series analysis abstract multiscale entropy mse is a prevalent algorithm used to measure the complexity of a time series because the coarse graining procedure reduces the length of a time series the conventional mse algorithm applied to a short term time series may yield an imprecise estimation of entropy or induce undefined entropy to overcome this obstacle the modified multiscale entropy mmse was developed the coarse graining procedure was replaced with a moving average procedure and a time delay was incorporated for constructing template vectors in calculating sample entropy for conducting short term time series analysis this study shows that the mmse algorithm is more reliable than the conventional mse

existence of multiple solutions for some nonlinear boundary value problems abstract by imposing one sided conditions on the nonlinearity where neither regularity nor uniformity is required we prove the existence of either a nonnegative or a nonpositive solution for first and second order ordinary differential equations with periodic neumann or dirichlet boundary conditions positone and nonpositone problems are considered some nonexistence results are also obtained when using generalized ambrosetti prodi type conditions we get the existence of nonnegative and nonpositive solutions for first and second order periodic or neumann boundary value problems our method of proof makes use of topological degree arguments in cones

upper and lower solutions and topological degree this paper deals with second order nonlinear boundary value problems we suppose the existence of upper and lower solutions of the problems which are well ordered i e the lower solution is less than the upper one and we also consider the case of upper and lower solutions having the opposite ordering we prove the relation between the topological degree and strict upper and lower solutions in both cases and using this we get the existence and multiplicity results for the boundary value problems under consideration

on rank driven dynamical systems we investigate a class of models related to the bak sneppen bs model initially proposed to study evolution the bs model is extremely simple and yet captures some forms of complex behavior such as self organized criticality that is often observed in physical and biological systems in this model random fitnesses in 0 1 are associated to agents located at the vertices of a graph g their fitnesses are ranked from worst 0 to best 1 at every time step the agent with the worst fitness and some others with a priori given rank probabilities are replaced by new agents with random fitnesses we consider two cases the exogenous case where the new fitnesses are taken from an a priori fixed distribution and the endogenous case where the new fitnesses are taken from the current distribution as it evolves we approximate the dynamics by making a simplifying independence assumption we use order statistics and dynamical systems to define a rank driven dynamical system that approximates the evolution of the distribution of the fitnesses in these rank driven models as well as in the bs model for this simplified model we can find the limiting marginal distribution as a function of the initial conditions agreement with experimental results of the bs model is excellent

length scales and power laws in the two dimensional forest fire model abstract we re examine a two dimensional forest fire model via monte carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two point correlation function of trees we check resp improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode we also investigate the possibility of describing the critical point in terms of a distribution of the global density we find that some qualitative features such as a temporal oscillation and a power law of the cluster size distribution can nicely be obtained from such a model that discards the spatial structure

cluster diversity and entropy on the percolation model the lattice animal identification algorithm we present an algorithm to identify and count different lattice animals la s in the site percolation model this algorithm allows a definition of clusters based on the distinction of cluster shapes in contrast with the well known hoshen kopelman algorithm in which the clusters are differentiated by their sizes it consists in coding each unit cell of a cluster according to the nearest neighbors nn and ordering the codes in a proper sequence in this manner a la is represented by a specific code sequence in addition with some modification the algorithm is capable of differentiating between fixed and free la s the enhanced hoshen kopelman algorithm j hoshen m w berry and k s minser phys rev e 56 1455 1997 is used to compose the set of nn code sequences of each cluster using monte carlo simulations on planar square lattices up to 2000x2000 we apply this algorithm to the percolation model we calculate the cluster diversity and cluster entropy of the system which leads to the determination of probabilities associated with the maximum of these functions we show that these critical probabilities are associated with the percolation transition and with the complexity of the system

the lower bounds of t periodic solutions for the forced duffing equation abstract this paper is devoted to the discussion of the number of t periodic solutions for the forced duffing equation x kx g t x s 1 h t with g t x being a continuous function by using the degree theory upper and lower solutions method and the twisting theorem

reshape scale method a novel multi scale entropic analysis approach abstract the reshape scale rs method was introduced in this article as a novel approach to perform multi scale transition of sample entropy this method was able to quantify the orderliness in the signal by determining the distance over which the subsequent data points can remain affiliated to one another entropic half life enhl was introduced to characterize such an affiliation the method was tested for 1 f processes for different values furthermore the dependency of the multi scale entropy analysis developed by costa et al 2002 6 to the probability density function and the standard deviation of autoregressive signals was studied and discussed

critical properties of the one dimensional forest fire model abstract a one dimensional forest fire model including lightnings is studied numerically and analytically for the tree correlation function a new correlation length with critical exponent v 5 6 is found by simulations a hamiltonian formulation is introduced which enables one to study the stationary state close to the critical point using quantum mechanical perturbation theory with this formulation also the structure of the low lying relaxation spectrum and the critical behaviour of the smallest complex gap are investigated numerically finally it is shown that critical correlation functions can be obtained from a simplified model involving only the total number of trees although such simplified models are unable to reproduce the correct off critical behaviour

asymmetric dynamics and critical behavior in the bak sneppen model abstract we investigate using mean field theory and simulation the effect of asymmetry on the critical behavior and probability density of bak sneppen models two kinds of anisotropy are investigated i different numbers of sites to the left and right of the central minimum site are updated and ii sites to the left and right of the central site are renewed in different ways of particular interest is the crossover from symmetric to asymmetric scaling for weakly asymmetric dynamics and the collapse of data with different numbers of updated sites but the same degree of asymmetry all non symmetric rules studied fall independent of the degree of asymmetry in the same universality class conversely symmetric variants reproduce the exponents of the original model our results confirm the existence of two symmetry based universality classes for extremal dynamics

generating synthetic time series from bak sneppen co evolution model mixtures abstract the bak sneppen model of co evolution is used to derive synthetic time series with a priori specified fractal dimension or hurst exponent through a mixing of processes in various lattice dimensions both theoretical and numerical analyses concern the avalanches at the critical threshold and provide a model for time series reconstruction that can be tested as an alternative to the classical fractional brownian motion fbm because of differences in properties new results on critical threshold and avalanche structure are obtained up to euclidean dimension d 6 the method involves a lattice based structure and therefore is suitable for the application of parallel computing

a multiplicity result for a nonlinear boundary value problem abstract in this paper we establish existence and multiplicity results for the problemx x f t x x s t a e in 0 x 0 x under the ambrosetti prodi type condition withfbeing a caratheodory function

existence and multiplicity of solutions for four point boundary value problems at resonance abstract this paper deals with the second order four point boundary value problem x t f t x t 0 t 1 x 0 ax x 1 bx where f 0 1 r r is continuous 0 1 0 a 1 1 0 b 1 a 1 b 1 a s 1 b 0 by using the coincidence degree theory the method of lower and upper solutions is established as applications some existence and multiplicity results are obtained

entropic sampling and natural selection in biological evolution with a view to connecting random mutation on the molecular level to punctuated equilibrium behaviour on the phenotype level we propose a new model for biological evolution which incorporates random mutation and natural selection in this scheme the system evolves continuously into new configurations yielding non stationary behaviour of the total fitness furthermore both the waiting time distribution of species and the avalanche size distribution display power law behaviours with exponents close to two which are consistent with the fossil data these features are rather robust indicating the key role of entropy

on singular probability densities generated by extremal dynamics abstract extremal dynamics is the mechanism that drives the bak sneppen model into a self organized critical state marked by a singular stationary probability density p x with the aim of understanding this phenomenon we study the bs model and several variants via mean field theory and simulation in all cases we find that p x is singular at one or more points as a consequence of extremal dynamics furthermore we show that the extremal barrier x i always belongs to the prohibited interval in which p x 0 our simulations indicate that the bak sneppen universality class is robust with regard to changes in the updating rule we find the same value for the exponent for all variants mean field theory which furnishes an exact description for the model on a complete graph reproduces the character of the probability distribution found in simulations for the modified processes mean field theory takes the form of a functional equation for p x

on the thresholds probability densities and critical exponents of bak sneppen like models abstract we report a simple method to accurately determine the threshold and the exponent of the bak sneppen bs model and also investigate the bs universality class for the random neighbor version of the bs model we find the threshold x 0 33332 3 in agreement with the exact result x 1 3 given by mean field theory for the one dimensional original model we find x 0 6672 2 in good agreement with the results reported in the literature for the anisotropic bs model we obtain x 0 7240 1 we study the finite size effect x l x l l observed in a system with l sites and find 1 00 1 for the random neighbor version 1 40 1 for the original model and 1 58 1 for the anisotropic case finally we discuss the effect of defining the extremal site as the one which minimizes a general function f x instead of simply f x x as in the original updating rule we emphasize that models with extremal dynamics have singular stationary probability distributions p x our simulations indicate the existence of two symmetry based universality classes

branching process in a stochastic extremal model we considered a stochastic version of the bak sneppen model sbsm of ecological evolution where the number m of sites mutated in a mutation event is restricted to only two here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion the critical behavior of the sbsm is found to be the same as the bs model in dimensions d 1 and 2 however on the scale free graphs the critical fitness value is nonzero even in the thermodynamic limit but the critical behavior is mean field like finally m has been made even smaller than two by probabilistically updating the mutation zone which also shows the original bs model behavior we conjecture that a sbsm on any arbitrary graph with any small branching factor greater than unity will lead to a self organized critical state

analytic results for scaling function and moments for a different type of avalanche in the bak sneppen evolution model starting from the master equation for the hierarchical structure of avalanches of a different kind within the frame of the bak sneppen evolution model we derive the exact formula of the scaling function describing the probability distribution of avalanches the scaling function displays features required by the scaling ansatz and verified by simulations using the scaling function we investigate the avalanche moment denoted by s k ensuremath delta overline f it is found that for any non negative integer k s k ensuremath delta overline f diverges as ensuremath delta f ensuremath k which gives an infinite group of exact critical exponents simulation outcomes of avalanche moments with k 1 2 3 are found to be consistent with the corresponding analytical results

criticality in simple models of evolution we consider two apparently similar models of biological evolution that have been claimed to exhibit self organized critical behavior a careful reanalysis of these models including several analytic results for one of them suggests that they are qualitatively different we demonstrate the limitations of the mean field description of these systems we argue that a more precise definition of self organized criticality is desirable and establish several criteria in this connection

existence and multiplicity results for some three point boundary value problems abstract using the method of upper and lower solutions and some degree theory arguments we establish the existence of at least three solutions of some second order nonlinear differential equations of the type x f t x x t i 0 1 subject to nonlinear three point boundary conditions x 0 0 x 1 g x 0 1 the growth of f with respect to x is allowed to be quadratic

triple positive solutions for nonlinear boundary value problems in banach space in this paper by applying two pairs of lower and upper solutions method and the topological degree theory of strict set contractions the existence of at least three positive solutions to m point boundary value problems for second order ordinary differential equations in banach spaces is obtained

different hierarchy of avalanches observed in the bak sneppen evolution model a quantity overline f denoting the average fitness of an ecosystem is introduced in the bak sneppen model through this quantity a different hierarchy of avalanches f 0 avalanche is observed in the evolution of bak sneppen model an exact gap equation governing the self organization of the model is presented in terms of overline f it is found that self organized threshold f c can be exactly obtained two basic exponents of the new avalanche ensuremath tau avalanche distribution and d avalanche dimension are given through simulations of one and two dimensional bak sneppen models it is suggested that overline f may be a good quantity in determining the emergence of criticality

existence of at least three solutions of nonlinear three point boundary value problems with super quadratic growth abstract we establish the existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type x f t x x 0 t 1 x 0 0 x 1 x 0 1 0 1 we employ a condition weaker than the well known nagumo condition which allows the nonlinearity f t x x to grow faster than quadratically with respect to x in some cases our method uses some degree theory arguments

correlations in the bak sneppen model from detrended fluctuation analysis abstract the correlations in the bak sneppen bs model are studied from fluctuations of three variables with detrended fluctuation analysis method similar scaling behaviors of the detrended fluctuations are found for the series of the minimum fitness in one and two dimensional 1d and 2d bs models the root mean square detrended fluctuations increase in a power law with the box size for the series of the location of the minimum fitness and the number of active sites the detrended fluctuations increase first for small box sizes and then saturate for large box sizes the power spectrum for the series of the number of active sites is shown to be a typical 1 f behavior for both the 1d and 2d bs models

absorbing state phase transitions with extremal dynamics extremal dynamics represents a path to self organized criticality in which the order parameter is tuned to a value of zero the order parameter is associated with a phase transition to an absorbing state given a process that exhibits a phase transition to an absorbing state we define an extremal absorbing process providing the link to the associated extremal nonabsorbing process stationary properties of the latter correspond to those at the absorbing state phase transition in the former studying the absorbing version of an extremal dynamics model allows to determine certain critical exponents that are not otherwise accessible in the case of the bak sneppen bs model the absorbing version is closely related to the f avalanche introduced by paczuski maslov and bak phys rev e 53 414 1996 or in spreading simulations to the bs branching process also studied by these authors the corresponding nonextremal process belongs to the directed percolation universality class we revisit the absorbing bs model obtaining refined estimates for the threshold and critical exponents in one dimension we also study an extremal version of the usual contact process using mean field theory and simulation the extremal condition slows the spread of activity and modifies the critical behavior radically defining an extremal directed percolation universality class of absorbing state phase transitions asymmetric updating is a relevant perturbation for this class even though it is irrelevant for the corresponding nonextremal class

bak sneppen type models and rank driven processes the bak sneppen model is a well known stochastic model of evolution that exhibits self organized criticality only a few analytical results have been established for it so far we report a surprising connection between bak sneppen type models and more tractable markov processes that evolve without any reference to an underlying topology specifically we show that in the case of a large number of species the long time behavior of the fitness profile in the bak sneppen model can be replicated by a model with a purely rank based update rule whose asymptotics can be studied rigorously

multiplicity of sign changing solutions for some four point boundary value problem abstract in this paper we obtain using leray schauder degree theory some multiplicity results for sign changing solutions of a four point boundary value problem we assume the existence of a pair of strict lower and upper solutions and some additional conditions on the nonlinear term f

bak sneppen model near zero dimension we consider the bak sneppen model near zero dimension where the avalanche exponent tau is close to 1 and the exponents m and sigma are close to 0 we demonstrate that tau 1 m sigma exp m 1 gamma small middle dot small middle dot small middle dot in this limit where gamma is euler s constant the avalanche hierarchy equation is rewritten in a form that makes it possible to find the relation between the critical exponents sigma and m with high accuracy we obtain precise values of the critical exponents for the one and two dimensional bak sneppen model and for the one dimensional anisotropic bak sneppen model

existence and approximation of solutions of second order nonlinear four point boundary value problems abstract we study some four point boundary value problems we use the method of upper and lower solutions to improve some previous existence results and apply the generalized method of quasilinearization to obtain a monotone sequence of iterates converging uniformly and rapidly to a solution of the problem

criticality and long range correlations in time series in classical and quantum systems we present arguments which indicate that a transitional state in between two different regimes implies the occurrence of 1 f time series and that this property is generic in both classical and quantum systems our study focuses on two particular examples the one dimensional module 1 logistic map and nuclear excitation spectra obtained with a schematic shell model hamiltonian we suggest that a transitional point is characterized by the long range correlations implied by 1 f time series we apply a fourier spectral analysis and the detrended fluctuation analysis method to study the fluctuations to each system

mean field theory for a simple model of evolution a simple dynamical model for darwinian evolution on its slowest time scale is analyzed its mean field theory is formulated and solved a random neighbor version of the model is simulated as is a one dimensional version in one dimension the dynamics can be described in terms of a repetitious random walker and anomalous diffusion with exponent 0 4 in all cases the model self organizes to a robust critical attractor

convergence dynamics of the bak sneppen model activity rate and waiting time distribution abstract in this work we study the convergence dynamics of two independent random configurations of the bak sneppen model of self organized criticality evolving under the same external noise a recently proposed measure of the hamming distance which considers the minimum difference between displaced configurations is used the displacement evolves in time intermittently we compute the jump activity rate and waiting time distribution and report on their asymptotic power law scaling which characterizes the slow relaxation and the absence of typical length and time scales typical of critical dynamical systems

exact equations and scaling relations for f0 avalanche in the bak sneppen evolution model an infinite hierarchy of exact equations is derived for the newly observed f0 avalanche in the bak sneppen model by solving the first order exact equation we find that the critical exponent gamma governing the divergence of the average avalanche size is exactly 1 for all dimensions which has been confirmed by extensive simulations solution of the gap equation yields another universal result rho 1 rho is the exponent of relaxation to attractor scaling relations are established among the critical exponents gamma tau d sigma and nu for the f0 avalanche