extended mean field study of a stochastic cellular automaton extended mean field theory is used for studying the one dimensional stochastic cellular automaton with rule 18 defined by wolfram rev mod phys 55 601 1983 the analysis is carried out at different levels taking n point and n pair correlations explicitly into consideration the pair approximations reproduce the exact results in the deterministic limit the critical behavior is studied by the pad e approximant method and the predicted critical probability and exponent agree with previous data within a few percent

prisoner s dilemma on a stochastic nongrowth network evolution model we investigate the evolution of cooperation on a nongrowth dynamic network model with a death birth dynamics based on tournament selection in the limit of large population size the equilibrium cooperator density is well described by our mean field approximations and inversely related to the average degree in the system small populations are also examined and found to deviate considerably from their expected mean field behavior an expanded replicator equation incorporating gaussian fluctuations in the strategy densities is then constructed with its output agreeing well with our simulation data for all sizes we also briefly comment on the role of strategy mutation in sustaining polymorphic populations in small systems

diversity of neighborhoods promotes cooperation in evolutionary social dilemmas abstract explaining the evolution of cooperative behavior is one of the most important and interesting problems in a myriad of disciplines such as evolutionary biology mathematics statistical physics social science and economics up to now there have been a great number of works aiming to this issue with the help of evolutionary game theory however vast majority of existing literatures simply assume that the interaction neighborhood and replacement neighborhood are symmetric which seems inconsistent with real world cases in this paper we consider the asymmetrical neighborhood player of type a whose factor is controlled by a parameter has four interaction neighbors and four replacement neighbors while player of type b whose factor is controlled by a parameter 1 possess eight interaction neighbors and four replacement neighbors by means of numerous monte carlo simulations we found that middle can make the cooperation reach the highest level while for this finding its robustness can be further validated in more games

forced lattice vibrations part ii this is the first part of a two part series on forced lattice vibrations in which a semi infinite lattice of one dimensional particles xn n 1 is driven from one end by a particle x0 this particle undergoes a given periodically perturbed uniform motion x0 t at h yt where a and are constants and h has period 2 for a wide variety of restoring forces f i e f 0 numerical calculations indicate the existence of a sequence of thresholds 1 1 a h f 2 2 a h f k k a h f k 0 as k if k k 1 a k phase wave that is well described by the wave form emerges and travels through the lattice the goal of this series is to describe the emergence and calculate some properties of these wave forms in part i the authors first consider the case where f x ex i e toda forces but h is arbitrary and show how to compute a basic diagnostic see j formula 1 26 for the system in terms of the solution of an associated scalar riemann hilbert problem once a certain finite set of numbers is known in another direction the authors consider the case where f x is restoring but arbitrary and h is small here the authors prove a general result asserting that if there exists a sufficiently ample family of traveling wave solutions of the doubly infinite lattice then it is possible to construct time periodic k phase wave solutions with asymptotics in n of type iii for the driven system i in part ii the authors prove that sufficiently ample families of traveling wave solutions of the system iv exist in the cases 1 and 1 2 for general restoring forces f in the case with toda forces f x ex the authors prove that sufficiently ample families of traveling wave solutions

on finite potential games a linear system called the potential equation pe is presented it is proved that a finite game is potential if and only if its potential equation has solution some properties of the potential equation are obtained based on these properties a closed form solution of the pe is obtained moreover a formula based on the solution of the pe is obtained to calculate the potential function finally it is proved that a networked evolutionary game is potential if and only if its fundamental network game is potential some interesting examples are presented to illustrate the theoretical results

on hamiltonian perturbations of hyperbolic systems of conservation laws ii universality of critical behaviour hamiltonian perturbations of the simplest hyperbolic equation u t a u u x 0 are studied we argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one should be essentially independent on the choice of generic perturbation neither on the choice of generic solution moreover this behaviour is described by a special solution to an integrable fourth order ode

why nonconservative schemes converge to wrong solutions error analysis this paper attempts to give a qualitative and quailtitative description of the numerical error introduced by using finite difference schemes in nonconservative form for scalar conservation laws we show that these schemes converge strongly in li norm to the solution of an inhomogeneous conservation law containing a borel measure source term moreover we analyze the properties of this borel measure and derive a sharp estimate for the l1 error between the limit function given by the scheme and the correct solution in general the measure source term is of the order of the entropy dissipation measure associated with the scheme in certain cases the error can be small for short times which makes it difficult to detect numerically but generically such an error will grow in time and this would lead to a large error for large time calculations finally we show that a local correction of any high order accurate scheme in nonconservative form is sufficient to ensure its convergence to the correct solution

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

the semiclassical limit of the defocusing nls hierarchy we establish the semiclassical limit of the one dimensional defocusing cubic nonlinear schrodinger nls equation complete integrability is exploited to obtain a global characterization of the weak limits of the entire nls hierarchy of conserved densities as the field evolves from reflectionless initial data under all the associated commuting flows consequently this also establishes the zero dispersion limit of the modified korteweg de vries equation that resides in that hierarchy we have adapted and clarified the strategy introduced by lax and levermore to study the zero dispersion limit of the korteweg de vries equation expanding it to treat entire integrable hierarchies and strengthening the limits obtained a crucial role is played by the convexity of the underlying log determinant with respect to the times associated with the commuting flows c 1999 john wiley sons inc

stochasticity and evolutionary stability in stochastic dynamical systems different concepts of stability can be obtained in different limits a particularly interesting example is evolutionary game theory which is traditionally based on infinite populations where strict nash equilibria correspond to stable fixed points that are always evolutionarily stable however in finite populations stochastic effects can drive the system away from strict nash equilibria which gives rise to a new concept for evolutionary stability the conventional and the new stability concepts may apparently contradict each other leading to conflicting predictions in large yet finite populations we show that the two concepts can be derived from the frequency dependent moran process in different limits our results help to determine the appropriate stability concept in large finite populations the general validity of our findings is demonstrated showing that the same results are valid employing vastly different co evolutionary processes

insight into the so called spatial reciprocity up to now there have been a great number of studies that demonstrate the effect of spatial topology on the promotion of cooperation dynamics namely the so called spatial reciprocity however most researchers probably attribute it to the positive assortment of strategies supported by spatial arrangement in this paper we analyze the time course of cooperation evolution under different evolution rules interestingly a typical evolution process can be divided into two evident periods the enduring end period and the expanding exp period where the former features that cooperators try to endure defectors invasion and the latter shows that perfect c clusters fast expand their area we find that the final cooperation level relies on two key factors the formation of the perfect c cluster at the end of the end period and the expanding fashion of the perfect c cluster during the exp period for deterministic rule the smooth expansion of c cluster boundaries enables cooperators to reach a dominant state whereas the rough boundaries for stochastic rule cannot provide a sufficient beneficial environment for the evolution of cooperation moreover we show that expansion of the perfect c cluster is closely related to the cluster coefficient of interaction topology to some extent we present a viable method for understanding the spatial reciprocity mechanism in nature and hope that it will inspire further studies to resolve social dilemmas

effects of strategy migration direction and noise in the evolutionary spatial prisoner s dilemma spatial games are crucial for understanding patterns of cooperation in nature and to some extent society they are known to be more sensitive to local symmetries than e g spin models this paper concerns the evolution of the prisoner s dilemma game on regular lattices with three different types of neighborhoods char22 the von neumann moore and kagom e types we investigate two kinds of dynamics for the players to update their strategies that can be unconditional cooperator or defector depending on the payoff difference an individual can adopt the strategy of a random neighbor a voter model like dynamics vmld or impose its strategy on a random neighbor i e invasion process like dynamics ipld in particular we focus on the effects of noise in combination with the strategy dynamics on the evolution of cooperation we find that vmld compared to ipld better supports the spreading and sustaining of cooperation we see that noise has nontrivial effects on the evolution of cooperation maximum cooperation density can be realized either at a medium noise level in the limit of zero noise or in both these regions the temptation to defect and the local interaction structure determine the outcome especially in the low noise limit the local interaction plays a crucial role in determining the fate of cooperators we elucidate these both by numerical simulations and mean field cluster approximation methods

binary and ternary oscillations in a cubic numerical scheme abstract we study a central difference semi discretization of the cubic scalar conservation law both spatial period 2 binary and period 3 ternary oscillations are stationary solutions of this scheme and we find where each type is linearly stable we observe numerically the formation of ternary oscillations to the left of riemann shock initial data with ur 0 while binary oscillations form to the right of riemann rarefaction data having ul 0 we derive modulation equations for both wave patterns using them to show that binary oscillations generated by the scheme are numerical artifacts while computing an explicit solution for the ternary modulation equations for positive initial data the ternary modulation equations remain hyperbolic while the solutions enter an elliptic region for data of both signs conditions under which solutions of the ternary modulation equations can be inverted to yield period 3 oscillations are also discussed

existence and modulation of traveling waves in particles chains we consider an infinite particle chain whose dynamics are governed by the following system of differential equations where qn t is the displacement of the nth particle at time t along the chain axis and denotes differentiation with respect to time we assume that all particles have unit mass and that the interaction potential v between adjacent particles is a convex c function for this system we prove the existence of c time periodic traveling wave solutions of the form qn t q wt kn where q is a periodic function q z q z 1 the period is normalized to equal 1 and k are respectively the frequency and the wave number is the mean particle spacing and can be chosen to be an arbitrary parameter we present two proofs one based on a variational principle and the other on topological methods in particular degree theory for small amplitude waves based on perturbation techniques we describe the form of the traveling waves and we derive the weakly nonlinear dispersion relation for the fully nonlinear case when the amplitude of the waves is high we use numerical methods to compute the traveling wave solution and the non linear dispersion relation we finally apply whitham s method of averaged lagrangian to derive the modulation equations for the wave parameters k and 1999 john wiley sons inc

stochastic dynamics of the prisoner s dilemma with cooperation facilitators in the framework of the paradigmatic prisoner s dilemma game we investigate the evolutionary dynamics of social dilemmas in the presence of cooperation facilitators in our model cooperators and defectors interact as in the classical prisoner s dilemma where selection favors defection however here the presence of a small number of cooperation facilitators enhances the fitness reproductive potential of cooperators while it does not alter that of defectors in a finite population of size n the dynamics of the prisoner s dilemma with facilitators is characterized by the probability that cooperation takes over fixation probability by the mean times to reach the absorbing states these quantities are computed exactly using fokker planck equations our findings corroborated by stochastic simulations demonstrate that the influence of facilitators crucially depends on the difference between their density z and the game s cost to benefit ratio r when z r the fixation of cooperators is likely in a large population and under weak selection pressure invasion and replacement of defection by cooperation is favored by selection if b z r 1 z n 1 where 0 b 1 is the cooperation payoff benefit when z r the fixation probability of cooperators is exponentially enhanced by the presence of facilitators but defection is the dominating strategy

a computational approach to soliton solutions of the kadomtsev petviashvili equation in this paper we present a computational approach to develop soliton solutions of the nonlinear kadomtsev petviashvili equation our approach rests mainly on the adomian decomposition method to include few components of the decomposition series the proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type numerical examples are tested to illustrate the proposed scheme

effect of the spatial autocorrelation of empty sites on the evolution of cooperation abstract an evolutionary game model is constructed to investigate the spatial autocorrelation of empty sites on the evolution of cooperation each individual is assumed to imitate the strategy of the one who scores the highest in its neighborhood including itself simulation results illustrate that the evolutionary dynamics based on the prisoner s dilemma game pd depends severely on the initial conditions while the snowdrift game sd is hardly affected by that a high degree of autocorrelation of empty sites is beneficial for the evolution of cooperation in the pd whereas it shows diversification effects depending on the parameter of temptation to defect in the sd moreover for the repeated game with three strategies always defect alld tit for tat tft and always cooperate allc simulations reveal that an amazing evolutionary diversity appears for varying of parameters of the temptation to defect and the probability of playing in the next round of the game the spatial autocorrelation of empty sites can have profound effects on evolutionary dynamics equilibrium and oscillation and spatial distribution

the evolutionary public goods game on scale free networks with heterogeneous investment abstract the public goods game pgg is generally considered as a suitable paradigm to explain ubiquitous cooperative behavior in this study we investigated the evolutionary pgg on scale free networks and studied the effect of individual heterogeneity by setting the cooperator x an investment value correlated to its degree as i x n k x j k j where k x is the degree of x j runs over all players and is a tunable parameter it is shown that the cooperation level is remarkably promoted by negative values of whereas it is highly depressed by positive values of moreover the effect of environmental noise has also been investigated our result may sharpen the understanding of cooperation induced by the individual diversity

the decomposition method applied to systems of partial differential equations and to the reaction diffusion brusselator model in this work systems of linear and nonlinear partial differential equations and the reaction diffusion brusselator model are handled by applying the decomposition method the advantage of this work is twofold firstly the decomposition method reduces the computational work secondly in comparison with existing techniques the decomposition method is an improvement with regard to its accuracy and rapid convergence the decomposition method has the advantage of being more concise for analytical and numerical purposes

the small dispersion limit of the korteweg de vries equation ii in part i the scattering transform method is used to study the weak limit of solutions to the initial value problem for the korteweg devries kdv equation as the dispersion tends to zero in that limit the associated schrodinger operator becomes semiclassical so the exact scattering data is replaced by its corresponding wkb expressions only nonpositive initial data are considered in that case the limiting reflection coefficient vanishes the explicit solution of kay and moses for the reflectionless inverse transform is then analyzed and the weak limit valid for all time is characterized by a quadratic minimum problem with constraints this minimum problem is reduced to a riemann hilbert problem in function theory in parts ii and iii we use function theoretical methods to solve the riemann hilbert problem in terms of solutions to an auxiliary initial value problem the weak limit satisfies the kdv equation with the dispersive term dropped until its derivatives become infinite up to that time the weak limit is a strong l2 limit at later times the weak limit is locally described by whitham s averaged equations or more generally by the equations found by flaschka et al using multiphase averaging for large times behavior of the weak limit is studied directly from the minimum problem

large oscillations arising in a dispersive numerical scheme abstract we study the oscillatory behavior that arises in solutions of a dispersive numerical scheme for the hopf equation whenever the classical solution of the equation develops a singularity modulation equations are derived that describe period two oscillations so long as the solution of those equations takes values for which the equations are hyperbolic however those equations have an elliptic region that may be entered by its solutions in a finite time after which the corresponding period two oscillations are seen to break down this kind of phenomenon has not been observed for integrable schemes the generation and propagation of period two oscillations are asymptotically analyzed and a matching formula is found for the transition between oscillatory and nonoscillatory regions modulation equations are also presented for period three oscillations numerical experiments are carried out that illustrate our analysis

promoting cooperation by local contribution under stochastic win stay lose shift mechanism a b s t r a c t we introduce a stochastic win stay lose shift wsls mechanism into evolutionary prisoner s dilemma on small world networks at each time step after playing with all its immediate neighbors each individual gets a score to evaluate its performance in the game the score is a linear combination of an individual s total payoff i e individual gain from the group and local contribution to its neighbors i e individual donation to the group if one s actual score is not larger than its desired score aspiration it switches current strategy to the opposite one with the probability depending on the difference between the two scores under this stochastic wsls regime we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation we also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score for much low intensity of deterministic switch cooperation is to a large extent independent of learning rate and full cooperation can be reached when relative weight is not less than 0 5 otherwise cooperation level is affected by the value of learning rate besides we find that the cooperation level is not sensitive to the topological parameters to explain these simulation results we provide corresponding analytical results based on mean field approximation and find out that simulationresultsareincloseagreementwiththeanalyticalones ourworkmaybehelpful in understanding the cooperative behavior in social systems based on this stochastic wsls mechanism

cooperative behavior in evolutionary snowdrift games with the unconditional imitation rule on regular lattices we study an evolutionary snowdrift game with the unconditional imitation updating rule on regular lattices detailed numerical simulations establish the structure of plateaus and discontinuous jumps of the equilibrium cooperation frequency f c as a function of the cost to benefit ratio r by analyzing the stability of local configurations it is found that the transitions occur at values of r at which there are changes in the ranking of the payoffs to the different local configurations of agents using different strategies nonmonotonic behavior of f c r at the intermediate range of r is analyzed in terms of the formation of blocks of agents using the cooperative strategy that are stabilized by agents inside the block due to the updating rule for random initial condition with 50 50 agents of different strategies randomly dispersed cooperation persists in the whole range of r and the level of cooperation is higher than that in the well mixed case in a wide range of r these results are in sharp contrast to those based on the replicator updating rule the sensitivity to initial states with different fractions of cooperative agents is also discussed the results serve to illustrate that both the spatial structure and the updating rule are important in determining the level of cooperation in a competing population when extreme initial states are used where there are very few agents of a strategy in a background of the opposite strategy the result would depend on the stability of the clusters formed by the initially minority agents

influence of the variance of degree distributions on the evolution of cooperation in complex networks abstract we study how initial network structure affects the evolution of cooperation in a spatial prisoner s dilemma game the network structure is characterized by various statistical properties among those properties we focus on the variance of the degree distribution and inquire how it affects the evolution of cooperation by three methods of imitation for every method it was found that a scale free network does not always promote the evolution of cooperation and that there exists an appropriate value of the variance at which cooperation is optimal

evolutionary prisoner s dilemma game on hierarchical lattices an evolutionary prisoner s dilemma pd game is studied with players located on a hierarchical structure of layered square lattices the players can follow two strategies d defector and c cooperator and their income comes from pd games with the neighbors the adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference monte carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels q and by the temptation to defect according to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low q 4 for larger q however the highest frequency of cooperators occurs in the middle layers the four level hierarchical structure provides the highest average total income for the whole community

inertia in strategy switching transforms the strategy evolution a recent experimental study traulsen et al proc natl acad sci 107 2962 2010 shows that human strategy updating involves both direct payoff comparison and the cost of switching strategy which is equivalent to inertia however it remains largely unclear how such a predisposed inertia affects 2 2 games in a well mixed population of finite size to address this issue the inertia bonus strategy switching cost is added to the learner payoff in the fermi process we find how inertia quantitatively shapes the stationary distribution and that stochastic stability under inertia exhibits three regimes with each covering seven regions in the plane spanned by two inertia parameters we also obtain the extended 1 3 rule with inertia and the speed criterion with inertia these two findings hold for a population above two we illustrate the above results in the framework of the prisoner s dilemma game as inertia varies two intriguing stationary distributions emerge the probability of coexistence state is maximized or those of two full states are simultaneously peaked our results may provide useful insights into how the inertia of changing status quo acts on the strategy evolution and in particular the evolution of cooperation

phase diagrams for an evolutionary prisoner s dilemma game on two dimensional lattices the effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner s dilemma game with players located on the sites of different two dimensional lattices this system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive using monte carlo simulations and the generalized mean field approximations we have determined the phase boundaries critical points separating the two phases on the plane of the temperature noise and temptation to choose defection in the zero temperature limit the cooperation can be sustained only for those connectivity structures where three site clique percolation occurs

cooperation in the noisy case prisoner s dilemma game on two types of regular random graphs we have studied an evolutionary prisoner s dilemma game with players located on two types of random regular graphs with a degree of 4 the analysis is focused on the effects of payoffs and noise temperature on the maintenance of cooperation when varying the noise level and or the highest payoff the system exhibits a second order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive for the random regular graph and bethe lattice the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions although the measure of cooperation is enhanced by the absence of loops in the connectivity structure for low noise the optimal connectivity structure is built up from randomly connected triangles

evolutionary prisoner s dilemma game on a square lattice a simplified prisoner s game is studied on a square lattice when the players interacting with their neighbors can follow two strategies to cooperate c or to defect d unconditionally the players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference using monte carlo simulations and dynamical cluster techniques we study the density c of cooperators in the stationary state this system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect in the limits stackrel ensuremath rightarrow c 0 and 1 we have observed critical transitions belonging to the universality class of directed percolation

dispersive approximations in fluid dynamics we have compared the results of a von neumann richtmyer calculation with the weak limit of calculations performed by von neumann s original method although there are discernible differences they are surprisingly small we analyze von newmann s algorithm for solving the initial value problem for the lagrangian equations of compressible flow

wavelet methods to eliminate resonances in the galerkin truncated burgers and euler equations it is well known that solutions to the fourier galerkin truncation of the inviscid burgers equation and other hyperbolic conservation laws do not converge to the physically relevant entropy solution after the formation of the first shock this loss of convergence was recently studied in detail ray et al phys rev e 84 016301 2011 and traced back to the appearance of a spatially localized resonance phenomenon perturbing the solution in this work we propose a way to remove this resonance by filtering a wavelet representation of the galerkin truncated equations a method previously developed with a complex valued wavelet frame is applied and expanded to embrace the use of real valued orthogonal wavelet bases which we show to yield satisfactory results only under the condition of adding a safety zone in wavelet space we also apply the complex valued wavelet based method to the two dimensional euler equation problem showing that it is able to filter the resonances in this case as well

operator splitting methods for generalized korteweg de vries equations we apply the method of operator splitting on the generalized korteweg de vries kdv equation ut f u x uxxx 0 by solving the nonlinear conservation law ut f u x 0 and the linear dispersive equation ut uxxx 0 sequentially we prove that if the approximation obtained by operator splitting converges then the limit function is a weak solution of the generalized kdv equation convergence properties are analyzed numerically by studying the effect of combining different numerical methods for each of the simplified problems

on a nonlinear hyperbolic variational equation ii the zero viscosity and dispersion limits we consider viscosity and dispersion regularizations of the nonlinear hyperbolic partial differential equation u t uux x 1 2u x 2 with the simplest initial data such that u x blows up in finite time we prove that the zero viscosity limit selects a unique global weak solution of the partial differential equation without viscosity we also present numerical experiments which indicate that the zero dispersion limit selects a different global weak solution of the same initial value problem

the role of mixed strategies in spatial evolutionary games abstract we study three strategy evolutionary games on a square lattice when the third strategy is a mixed strategy of the first and second ones it is shown that the resultant three strategy game is a potential game as well as its two strategy version evaluating the potential we derive a phase diagram on a two dimensional plane of rescaled payoff parameters that is valid in the zero noise limit of the logit dynamical rule the mixed strategy is missing in this phase diagram the effects of two different dynamical rules are analyzed by monte carlo simulations and the results of imitation dynamics indicate the dominance of the mixed strategy within the region of the hawk dove game where it is an evolutionarily stable strategy the effects and consequences of the different dynamical rules on the final stationary states and phase transitions are discussed

resonance phenomenon for the galerkin truncated burgers and euler equations it is shown that the solutions of inviscid hydrodynamical equations with suppression of all spatial fourier modes having wave numbers in excess of a threshold k mathrm g exhibit unexpected features the study is carried out for both the one dimensional burgers equation and the two dimensional incompressible euler equation for large k mathrm g and smooth initial conditions the first symptom of truncation a localized short wavelength oscillation which we call a tyger is caused by a resonant interaction between fluid particle motion and truncation waves generated by small scale features shocks layers with strong vorticity gradients etc these tygers appear when complex space singularities come within one galerkin wavelength ensuremath lambda mathrm g 2 ensuremath pi k mathrm g from the real domain and typically arise far away from preexisting small scale structures at locations whose velocities match that of such structures tygers are weak and strongly localized at first in the burgers case at the time of appearance of the first shock their amplitudes and widths are proportional to k mathrm g ensuremath 2 3 and k mathrm g ensuremath 1 3 respectively but grow and eventually invade the whole flow they are thus the first manifestations of the thermalization predicted by t d lee q j appl math 10 69 1952 the sudden dissipative anomaly the presence of a finite dissipation in the limit of vanishing viscosity after a finite time t ensuremath star which is well known for the burgers equation and sometimes conjectured for the three dimensional euler equation has as counterpart in the truncated case the ability of tygers to store a finite amount of energy in the limit k mathrm g ensuremath rightarrow ensuremath infty this leads to reynolds stresses acting on scales larger than the galerkin wavelength and thus prevents the flow from converging to the inviscid limit solution there are indications that it may eventually be possible to purge the tygers and thereby to recover the correct inviscid limit behavior

re entrant behaviour in the domany kinzel cellular automaton we present numerical and analytical results for a special kind of one dimensional probabilistic cellular automaton the so called domany kinzel automaton it is shown that the phase boundary separating the active and the recently found chaotic phase exhibits re entrant behaviour furthermore exact results for the p2 0 line are discussed

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

local structure theory for cellular automata abstract the mean field theory for cellular automata wolfram and schulman and seiden is generalized to the local structure theory the local structure theory is a sequence of finitely parameterized models of the statistical features of a cellular automaton s evolution the n th model in the sequence takes into account correlations in terms of the probability of blocks of n states a class of measures the n block measures is introduced the local structure operator of order n maps n block measures to n block measures in a manner which reflects the cellular automaton map on blocks of states the fixed points of the map on measures approximate the invariant measures of the cellular automaton the ability of the local structure theory to model evolution from uncorrelated initial distributions is studied the theory gives exact results in simple cases in more complex cases monte carlo numerical experiments suggest that an accurate statistical portrait of cellular automaton evolution is obtained the invariant measures of a cellular automaton and the stability of these measures may be obtained from the local structure theory the local structure theory appears to be a powerful method for characterization and classification of cellular automata nearest neighbor cellular automata with two states per cell are studied using this method

binary modulated oscillations in a semi discrete version of burgers equation abstract in this paper we study both analytically and numerically the binary modulated oscillations which arise in an integrable semi discrete approximation to inviscid burgers explicit solutions of the binary modulation equations derived in goodman and lax 1988 are found for several choices of initial data observations based on numerical experiments are presented as to which initial data lead to solutions containing purely binary oscillations comparisons are made to the integrable theory of the kac van moerbeke and toda lattices non integrable schemes for which the binary oscillations also remain hyperbolic are presented and explicit solutions of their binary modulation equations are found

universality of weak selection weak selection which means a phenotype is slightly advantageous over another is an important limiting case in evolutionary biology recently it has been introduced into evolutionary game theory in evolutionary game dynamics the probability to be imitated or to reproduce depends on the performance in a game the influence of the game on the stochastic dynamics in finite populations is governed by the intensity of selection in many models of both unstructured and structured populations a key assumption allowing analytical calculations is weak selection which means that all individuals perform approximately equally well in the weak selection limit many different microscopic evolutionary models have the same or similar properties how universal is weak selection for those microscopic evolutionary processes we answer this question by investigating the fixation probability and the average fixation time not only up to linear but also up to higher orders in selection intensity we find universal higher order expansions which allow a rescaling of the selection intensity with this we can identify specific models which violate linear weak selection results such as the one third rule of coordination games in finite but large populations

on evolutionary spatial heterogeneous games abstract how cooperation between self interested individuals evolve is a crucial problem both in biology and in social sciences that is far from being well understood evolutionary game theory is a useful approach to this issue the simplest model to take into account the spatial dimension in evolutionary games is in terms of cellular automata with just a one parameter payoff matrix here the effects of spatial heterogeneities of the environment and or asymmetries in the interactions among the individuals are analysed through different extensions of this model instead of using the same universal payoff matrix bimatrix games in which each cell at site i j has its own different temptation to defect parameter t i j are considered first the case in which these individual payoffs are constant in time is studied second an evolving evolutionary spatial game such that t t i j t i e besides depending on the position evolves by natural selection is used to explore the combination of spatial heterogeneity and natural selection of payoff matrices

evolutionary prisoner s dilemma game on weighted scale free networks this paper investigates the evolutionary prisoner s dilemma on weighted scale free networks the weighted networks are generated by adopting barabscale free network and assigning link weight with wij ki kj simulation results show thatthe cooperationfrequency hasa strongdependence on the value of which isassociated withthe maximalcooperation frequency has been sought out moreover gini coefficient and pareto exponent of the system s wealth distribution are investigated the inequality of wealth distribution is minimized at 1

cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner s dilemma games we study an evolutionary prisoner s dilemma game with two layered graphs where the lower layer is the physical infrastructure on which the interactions are taking place and the upper layer represents the connections for the strategy adoption learning mechanism this system is investigated by means of monte carlo simulations and an extended pair approximation method we consider the average density of cooperators in the stationary state for a fixed interaction graph while varying the number of edges in the learning graph according to the monte carlo simulations the cooperation is modified substantially in a way resembling a coherence resonance like behavior when the number of learning edges is increased this behavior is reproduced by the analytical results

evolutionary dynamics on graphs efficient method for weak selection investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time here we propose an efficient method to study any type of game on arbitrary graph structures for weak selection in this limit evolutionary game dynamics represents a first order correction to neutral evolution spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations this framework is then applied to one of the most intriguing questions in evolutionary biology the evolution of cooperation we demonstrate that degree heterogeneity of a graph impedes cooperation and that the success of tit for tat not only depends on the number of rounds but also on the degree of the graph moreover considering the mutation selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths in particular degree heterogeneity a prominent feature of scale free networks generally results in a more pronounced increase of the critical benefit to cost ratio required for evolution to favor cooperation as compared to regular graphs this conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general 2 2 games for different types of graphs computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies

the zero dispersion limit a deterministic analogue of turbulence weak limits of oscillatory sequences of dispersive compressible flows show a remarkable resemblance to the ensemble averages of classical turbulence theory how much relevance such ideas have for incompressible flows is not clear

dispersive shock waves and modulation theory there is growing physical and mathematical interest in the hydrodynamics of dissipationless dispersive media since g b whitham s seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics there has been a significant body of work in this area however there has been no comprehensive survey of the field of dispersive hydrodynamics utilizing whitham s averaging theory as the primary mathematical tool we review the rich mathematical developments over the past fifty years with an emphasis on physical applications the fundamental large scale coherent excitation in dispersive hydrodynamic systems is an expanding oscillatory dispersive shock wave or dsw both the macroscopic and microscopic properties of dsws are analyzed in detail within the context of the universal integrable and foundational models for uni directional korteweg de vries equation and bi directional nonlinear schrodinger equation dispersive hydrodynamics a dsw fitting procedure that does not rely upon integrable structure yet reveals important macroscopic dsw properties is described dsw theory is then applied to a number of physical applications superfluids nonlinear optics geophysics and fluid dynamics finally we survey some of the more recent developments including non classical dsws dsw interactions dsws in perturbed and inhomogeneous environments and two dimensional oblique dsws

numerical doubly periodic solution of the kdv equation with the initial condition via the decomposition method in this paper a scheme is extended to study numerical doubly periodic solutions of the kortweg de vries kdv equation with initial conditions using the adomian decomposition method as a result we obtain the numerical doubly periodic solutions of the kdv equation with initial conditions the numerical doubly periodic solution is compared with the exact doubly periodic solution moreover we analyze the absolute error and relative error between them and also give the contour and density plots of the numerical doubly periodic solutions with two different moduli m 15 78

modeling cooperative and competitive behaviors in emergency evacuation a game theoretical approach a game theoretical model to study evacuees cooperative and competitive behaviors during an emergency evacuation is proposed the model integrated with evacuation dynamics model determines the density of cooperative and competitive evacuees and their related evacuation times computer simulation results show that 1 as urgency of evacuation increases cooperation among evacuees decreases 2 in an emergency situation individual hyper rationality among evacuees diminishes evacuation efficiency 3 the imitation effect enhances cooperation among evacuees yet reduces evacuation efficiency this study provides a methodological pattern to research crowd behaviors in emergency evacuation

numerical solutions of coupled burgers equations with time and space fractional derivatives in this paper by introducing the fractional derivative in the sense of caputo the adomian decomposition method is directly extended to study the coupled burgers equations with time and space fractional derivatives as a result the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components the figures show the effectiveness and good accuracy of the proposed method

coevolutionary games on networks we study agents on a network playing an iterated prisoner s dilemma against their neighbors the resulting spatially extended coevolutionary game exhibits stationary states which are nash equilibria after perturbation of these equilibria avalanches of mutations reestablish a stationary state scale free avalanche distributions are observed that are in accordance with calculations from the nash equilibria and a confined branching process the transition from subcritical to critical avalanche dynamics can be traced to a change in the degeneracy of the cooperative macrostate and is observed for many variants of this game

on dispersive difference schemes i etude du comportement oscillatoire et de la convergence faible des solutions des approximations aux differences dispersives de u t 1 2 u 2 x 0

non classical shocks and kinetic relations scalar conservation laws this paper analyzes the non classical shock waves which arise as limits of certain diffusive dispersive approximations to hyperbolic conservation laws such shocks occur for non convex fluxes and connect regions of different convexity they have negative entropy dissipation for a single convex entropy function but not all convex entropies and do not obey the classical oleinik entropy criterion we derive necessary conditions for the existence of non classical shock waves and construct them as limits of traveling wave solutions for several diffusive dispersive approximations

numerical solutions for fractional kdv burgers equation by adomian decomposition method abstract based on the symbolic computation system maple adomian decomposition method developed for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional kdv burgers equation the fractional derivatives are described in the caputo sense according to my knowledge this paper represents the first available numerical solutions of the nonlinear fractional kdv burgers equation with time and space fractional derivatives finally the solutions of our model equation are calculated in the form of convergent series with easily computable components

effects of inhomogeneous activity of players and noise on cooperation in spatial public goods games we study the public goods game in the noisy case by considering the players with inhomogeneous activity of teaching on a square lattice it is shown that the introduction of the inhomogeneous activity of teaching the players can remarkably promote cooperation by investigating the effects of noise on cooperative behavior in detail we find that the variation of cooperator density c with the noise parameter displays several different behaviors c monotonically increases decreases with c first increases decreases with and then it decreases increases monotonically after reaching its maximum minimum value which depends on the amount of the multiplication factor r on whether the system is homogeneous or inhomogeneous and on whether the adopted updating is synchronous or asynchronous these results imply that the noise plays an important and nontrivial role in the evolution of cooperation