dilemma solving by the coevolution of networks and strategy in a 2 2 game a 2 ifmmode times else texttimes fi 2 game model implemented by a coevolution mechanism of both networks and strategy inspired by the work of zimmermann and eguiluz phys rev e72 056118 2005 is established network adaptation is the manner in which an existing link between two agents is destroyed and how a new one is established to replace it the strategy is defined as whether an agent offers cooperation c or defection d both the networks and strategy are synchronously renovated in a simulation time step a series of numerical experiments considering various 2 ifmmode times else texttimes fi 2 game structures reveals that the proposed coevolution mechanism can solve dilemmas in several game classes the effect of solving a dilemma means mutual cooperation reciprocity r reciprocity which is brought about by emerging several cooperative hub agents who have plenty of links this effect can be primarily observed in game classes of the prisoner s dilemma and stag hunt the coevolution mechanism however seems counterproductive for game classes of leader and hero where the alternating reciprocity st reciprocity is meaningful

enhanced convergence estimates for semi lagrangian schemes application to the vlasov poisson equation we prove enhanced error estimates for high order semi lagrangian discretizations of the vlasov poisson equation it provides new insights into optimal numerical strategies for the numerical solution of this problem the new error estimate o min frac delta x delta t 1 delta x p delta t 2 is based on advanced error estimates for semi lagrangian schemes also equal to shifted strang s schemes for the discretization of the advection equation

fixation transient landscape and diffusion dilemma in stochastic evolutionary game dynamics agent based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics both the ultimate fixation and the pre fixation transient behavior are important to a full understanding of the dynamics in this paper we study the transient dynamics of the well mixed moran process through constructing a landscape function it is shown that the landscape playing a central theoretical device that integrates several lines of inquiries the stable behavior of the replicator dynamics the long time fixation and continuous diffusion approximation associated with asymptotically large population several issues relating to the transient dynamics are discussed i multiple time scales phenomenon associated with intra and inter attractoral dynamics ii discontinuous transition in stochastically stationary process akin to maxwell construction in equilibrium statistical physics and iii the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics it is found that rare events with exponentially small probabilities corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics plays an important role in understanding the origin of the complexity in evolutionary nonlinear biological systems

promotion of cooperation by payoff noise in a 2 2 game a series of numerical simulations of a 2 ifmmode times else texttimes fi 2 symmetric game on a network examined whether payoff matrix noise promotes cooperation as reported initially by perc new j phys 8 22 2006 agents have no memory they offer cooperation c or defection d we assume that the network is time invariable the effect of payoff matrix noise pmn is measured by a simulated payoff difference between a normal network game and a network game with pmn the effect of pmn appears only when a local strategy adaptation is implemented for example a network game with imitation dynamics the influence of pmn becomes more significant with a larger stochastic deviation and less significant in a larger degree network one reason for pmn s effectiveness is the local strategy adaptation mechanism which helps both the preservation and fixation of c agents and not that the payoff matrix noise makes a dilemma game into a trivial dilemma free game

high order hamiltonian splitting for the vlasov poisson equations we consider the vlasov poisson equation in a hamiltonian framework and derive new time splitting methods based on the decomposition of the hamiltonian functional between the kinetic and electric energy assuming smoothness of the solutions we study the order conditions of such methods it appears that these conditions are of runge kutta nystrom type in the one dimensional case the order conditions can be further simplified and efficient methods of order 6 with a reduced number of stages can be constructed in the general case high order methods can also be constructed using explicit computations of commutators numerical results are performed and show the benefit of using high order splitting schemes in that context complete and self contained proofs of convergence results and rigorous error estimates are also given

analysis of an algorithm for the galerkin characteristic method it is shown that the interpretation of the galerkin characteristic method for the scalar advection equation in the framework of particle methods yields a computationally efficient algorithm such an algorithm consists of updating the dependent variable at the grid points by cubic spline interpolation at the feet of the characteristic curves the algorithm is unconditionally stable the error analysis in the maximum norm shows that for sufficiently smooth functions the feet of the characteristic curves are points of high order convergence

semi lagrangian schemes for the vlasov equation on an unstructured mesh of phase space a new scheme for solving the vlasov equation using an unstructured mesh for the phase space is proposed the algorithm is based on the semi lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves we use different local interpolation operators to reconstruct the distribution function f some of which need the knowledge of the gradient of f we can use limiter coefficients to maintain the positivity and the l bound of f and optimize these coefficients to ensure the conservation of the l1 norm that is to say the mass by solving a linear programming problem several numerical results are presented in two and three axisymmetric case dimensional phase space the local interpolation technique is well suited for parallel computation

iterated snowdrift game among mobile agents with myopic expected reward based decision rule numerical and analytical research abstract the iterated spatial game among the mobile population is an interesting problem in the fields of biological social and economic sciences inspired by some recent works this paper concentrates on the iterated snowdrift game among movable and myopic agents two different decision making schemes namely the utility maximum rule and the fermi rule are applied and examined in the former case cooperation is found to be enhanced by moving velocity with an upper bound the analytical results of the model are deduced at two extreme cases when agents cannot move or move quickly in the latter case the influences of velocity and temptation to defect are much more complicated these results allow a deeper insight of the related model as well as the emergence of cooperation

mixing protocols in the public goods game if interaction partners in social dilemma games are not selected randomly from the population but are instead determined by a network of contacts it has far reaching consequences for the evolutionary dynamics selecting partners randomly leads to a well mixed population where pattern formation is essentially impossible this rules out important mechanisms that can facilitate cooperation most notably network reciprocity in contrast if interactions are determined by a lattice or a network then the population is said to be structured where cooperators can form compact clusters that protect them from invading defectors between these two extremes however there is ample middle ground that can be brought about by the consideration of temporal networks mobility or other coevolutionary processes the question that we here seek to answer is when does mixing on a lattice actually lead to well mixed conditions to that effect we use the public goods game on a square lattice and we consider nearest neighbor and random mixing with different frequencies as well as a mix of both mixing protocols not surprisingly we find that nearest neighbor mixing requires a higher frequency than random mixing to arrive at the well mixed limit the differences between the two mixing protocols are most expressed at intermediate mixing frequencies whilst at very low and very high mixing frequencies the two almost converge we also find a near universal exponential growth of the average size of cooperator clusters as their fraction increases from zero to one regardless of whether this increase is due to increasing the multiplication factor of the public goods decreasing the frequency of mixing or gradually shifting the mixing from random to nearest neighbors

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

cooperation in two dimensional mixed games evolutionary game theory is a common framework to study the evolution of cooperation where it is usually assumed that the same game is played in all interactions here we investigate a model where the game that is played by two individuals is uniformly drawn from a sample of two different games using the master equation approach we show that the random mixture of two games is equivalent to play the average game when i the strategies are statistically independent of the game distribution and ii the transition rates are linear functions of the payoffs we also use monte carlo simulations in a two dimensional lattice and mean field techniques to investigate the scenario when the two above conditions do not hold we find that even outside of such conditions several quantities characterizing the mixed games are still the same as the ones obtained in the average game when the two games are not very different

enhancement of cooperation in highly clustered scale free networks we study the effect of clustering on the organization of cooperation by analyzing the evolutionary dynamics of the prisoner s dilemma on scale free networks with a tunable value of clustering we find on the one hand that a high value of the clustering coefficient produces an overall enhancement of cooperation in the network even for a very high temptation to defect on the other hand high clustering homogenizes the process of invasion of degree classes by defectors decreasing the chances of survival of low densities of cooperators in the network

the decomposition method applied to chandrasekhar h equation in this paper adomian s decomposition method is applied to the nonlinear chandrasekhar h equation the solution is expressed as an infinite series it is shown that two or three iterations are sufficient to obtain good approximation of the exact solution adomian s method has been illustrated by considering some particular cases of this nonlinear integral equation that are of physical interest

ordering in spatial evolutionary games for pairwise collective strategy updates evolutionary 2 ifmmode times else texttimes fi 2 games are studied with players located on a square lattice during the evolution the randomly chosen neighboring players try to maximize their collective income by adopting a random strategy pair with a probability dependent on the difference of their summed payoffs between the final and initial states assuming quenched strategies in their neighborhood in the case of the anticoordination game this system behaves like an antiferromagnetic kinetic ising model within a wide region of social dilemmas this dynamical rule supports the formation of similar spatial arrangement of the cooperators and defectors ensuring the optimum total payoff if the temptation to choose defection exceeds a threshold value dependent on the sucker s payoff the comparison of the results with those achieved for pairwise imitation and myopic strategy updates has indicated the relevant advantage of pairwise collective strategy update in the maintenance of cooperation

convergence analysis for a class of high order semi lagrangian advection schemes the convergence properties of a class of high order semi lagrangian schemes for pure advection equations are studied here in the framework of the theory of viscosity solutions we review the general convergence results for discrete time approximation schemes belonging to that class and we prove some a priori estimates in l infty and l2 for the rate of convergence of fully discrete schemes we prove then that a careful coupling of time and space discretizations can allow large time steps in the numerical integration still preserving the accuracy of the solutions several examples of schemes and numerical tests are presented

memory based snowdrift game on networks we present a memory based snowdrift game mbsg taking place on networks we found that when a lattice is taken to be the underlying structure the transition of spatial patterns at some critical values of the payoff parameter is observable for both four and eight neighbor lattices the transition points as well as the styles of spatial patterns can be explained by local stability analysis in sharp contrast to previously reported results cooperation is promoted by the spatial structure in the mbsg interestingly we found that the frequency of cooperation of the mbsg on a scale free network peaks at a specific value of the payoff parameter this phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation the memory effects of individuals are discussed in detail and some nonmonotonous phenomena are observed on both lattices and scale free networks our work may shed some new light on the study of evolutionary games over networks

analysis of a new class of forward semi lagrangian schemes for the 1d vlasov poisson equations the vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles it is self consistently coupled with poisson s equation which rules the evolution of the electric field in this paper we introduce a new class of forward semi lagrangian schemes for the vlasov poisson system based on a cauchy kovalevsky ck procedure for the numerical solution of the characteristic curves exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the ck scheme as for a more classical verlet scheme a l 1 convergence of the schemes will be proved error estimates in o left delta t 2 h 2 frac h 2 delta t right for verlet are obtained where t and h max x v are the discretization parameters

convergence of a semi lagrangian scheme for the one dimensional vlasov poisson system a semi lagrangian scheme is proposed for solving the periodic one dimensional vlasov poisson system in phase space on unstructured meshes the distribution function f t x v and the electric field e t x are shown to converge to the exact solution values in the l infty norm the rate of convergence is in o h4 3

communication scheme based on evolutionary spatial 2 2 games abstract a visual communication scheme based on evolutionary spatial 2 2 games is proposed in this paper self organizing patterns induced by complex interactions between competing individuals are exploited for hiding and transmitting secret visual information properties of the proposed communication scheme are discussed in details it is shown that the hiding capacity of the system the minimum size of the detectable primitives and the minimum distance between two primitives is sufficient for the effective transmission of digital dichotomous images also it is demonstrated that the proposed communication scheme is resilient to time backwards plain image attacks and is highly sensitive to perturbations of private and public keys several computational experiments are used to demonstrate the effectiveness of the proposed communication scheme

cooperation for volunteering and partially random partnerships competition among cooperative defective and loner strategies is studied by considering an evolutionary prisoner s dilemma game for different partnerships in this game each player can adopt one of its coplayer s strategy with a probability depending on the difference of payoffs coming from games with the corresponding coplayers our attention is focused on the effects of annealed and quenched randomness in the partnership for fixed number of coplayers it is shown that only the loners survive if the four coplayers are chosen randomly mean field limit on the contrary on the square lattice all the three strategies are maintained by the cyclic invasions resulting in a self organizing spatial pattern if the fixed partnership is described by a regular small world structure then a homogeneous oscillation occurs in the population dynamics when the measure of quenched randomness exceeds a threshold value similar behavior with higher sensitivity to the randomness is found if temporary partners are substituted for the standard ones with some probability at each step of iteration

role separating ordering in social dilemmas controlled by topological frustration three is a crowd is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models accordingly social relations within a triangle deserve special attention with this motivation we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice this topology provides an irreconcilable frustration which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game by using different strategy updating protocols we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb like organization which helps to minimize the negative consequence of the topological frustration we relate the emergence of these patterns to the microscopic dynamics of the evolutionary process both by means of mean field approximations and monte carlo simulations for comparison we also consider the same evolutionary dynamics on the square lattice where of course the topological frustration is absent however with the deletion of diagonal links of the triangular lattice we can gradually bridge the gap to the square lattice interestingly in this case the level of cooperation in the system is a direct indicator of the level of topological frustration thus providing a method to determine frustration levels in an arbitrary interaction network

higher order time splitting for the linear vlasov equation many semi lagrangian schemes for solving the vlasov equation use a second order time splitting method proposed by cheng and knorr in this paper a fourth order time splitting method is proposed this is combined with cubic spline interpolation in x and v and a rigorous ell 2 error bound is obtained for the linear vlasov equation in arbitrary space dimension also this method and that of cheng and knorr are implemented and compared for a test case in one space dimension

hawks and doves on small world networks we explore the hawk dove game on networks with topologies ranging from regular lattices to random graphs with small world networks in between this is done by means of computer simulations using several update rules for the population evolutionary dynamics we find the overall result that cooperation is sometimes inhibited and sometimes enhanced in those network structures with respect to the mixing population case the differences are due to different update rules and depend on the gain to cost ratio we analyze and qualitatively explain this behavior by using local topological arguments

evolutionary prisoner s dilemma game with dynamic preferential selection we study a modified prisoner s dilemma game taking place on two dimensional disordered square lattices the players are pure strategists and can either cooperate or defect with their immediate neighbors in the generations each player updates its strategy by following one of the neighboring strategies with a probability dependent on the payoff difference the neighbor selection obeys a dynamic preferential rule i e the more frequently a neighbor s strategy was adopted by the focal player in the previous rounds the larger probability it will be chosen to refer to in the subsequent rounds it is found that cooperation is substantially promoted due to this simple selection mechanism corresponding analysis is provided by the investigation of the distribution of the players impact weights persistence and correlation function

an investigation of the asymptotic decomposition method for nonlinear equations in physics this paper considers an interesting variation of the author s decomposition method first proposed in 1983 which permits determination of the behavior of the solution of a differential equation as the independent variable approaches infinity extensions to partial differential equations are also considered

degree mixing in multilayer networks impedes the evolution of cooperation traditionally the evolution of cooperation has been studied on single isolated networks yet a player especially in human societies will typically be a member of many different networks and those networks will play different roles in the evolutionary process multilayer networks are therefore rapidly gaining on popularity as the more apt description of a networked society with this motivation we here consider two layer scale free networks with all possible combinations of degree mixing wherein one network layer is used for the accumulation of payoffs and the other is used for strategy updating we find that breaking the symmetry through assortative mixing in one layer and or disassortative mixing in the other layer as well as preserving the symmetry by means of assortative mixing in both layers impedes the evolution of cooperation we use degree dependent distributions of strategies and cluster size analysis to explain these results which highlight the importance of hubs and the preservation of symmetry between multilayer networks for the successful resolution of social dilemmas

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

effect of memory on the prisoner s dilemma game in a square lattice we have studied the effect of memory on the evolution of the prisoner s dilemma game in square lattice networks based on extensive simulations we found that the density of cooperators was enhanced by an increasing memory effect for most parameters however we also observed that the density of cooperators decreased with an increased memory effect in the case of a large memory and moderate temptation it is interesting to note that memory makes cooperators immune from temptation the strength of protection reaches its maximal value only for a moderate memory effect

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

phase diagram of a model of self organizing hierarchies abstract we introduce a simple model of self organizing hierarchies in animal societies which relies on a basic positive feedback mechanism reinforcing the ability of a given individual to win or lose in a hierarchical interaction depending on how many times it won or lost in previous interactions if a forgetting strength is included which determines the rate at which events in the past are forgotten and no longer influence the force of an individual subcritical or supercritical bifurcations in the formation of the hierarchical structure are observed as the density of individuals is varied the nature of the transition is shown to depend on a parameter analogous to the inverse of a temperature defining the amount of determinism in the outcomes of the fights we therefore observe a dynamical tricritical point in the plane

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

spatial social dilemmas dilution mobility and grouping effects with imitation dynamics abstract we present an extensive systematic study of the prisoner s dilemma and snowdrift games on a square lattice under a synchronous noiseless imitation dynamics we show that for both the occupancy of the network and the random mobility of the agents there are intermediate values that may increase the amount of cooperators in the system and new phases appear we analytically determine the transition lines between these phases and compare with the mean field prediction and the observed behavior on a square lattice we point out which are the more relevant microscopic processes that entitle cooperators to invade a population of defectors in the presence of mobility and discuss the universality of these results

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

an approximate method for solving a class of weakly singular volterra integro differential equations abstract in this paper we present a new approach to resolve linear and nonlinear weakly singular volterra integro differential equations of first or second order by first removing the singularity using taylor s approximation and then transforming the given first or second order integro differential equations into an ordinary differential equation such as the well known legendre degenerate hypergeometric euler or abel equations in such a manner that adomian s asymptotic decomposition method can be applied which permits convenient resolution of these equations some examples with closed form solutions are studied in detail to further illustrate the proposed technique and the results obtained demonstrate this approach is indeed practical and efficient

a performance comparison of semi lagrangian discontinuous galerkin and spline based vlasov solvers in four dimensions abstract the purpose of the present paper is to compare two semi lagrangian methods in the context of the four dimensional vlasov poisson equation more specifically our goal is to compare the performance of the more recently developed semi lagrangian discontinuous galerkin scheme to cubic spline interpolation which is widely used in eulerian vlasov simulation to that end we perform simulations for nonlinear landau damping and a two stream instability and provide benchmarks for the selalib and sldg codes both on a workstation and using mpi on a cluster in addition we will present results for the graphic processing unit gpu implementation contained in sldg we find that the semi lagrangian discontinuous galerkin scheme shows a moderate improvement in run time for nonlinear landau damping and a substantial improvement for the two stream instability it should be emphasized that these results are markedly different from results obtained in the asymptotic regime which favor spline interpolation thus we conclude that the traditional approach of evaluating numerical methods is misleading even for short time simulations in addition the absence of any global communication in the semi lagrangian discontinuous galerkin method gives it a decisive advantage for scaling to more than 256 cores

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

convergence of a high order semi lagrangian scheme with propagation of gradients for the one dimensional vlasov poisson system in this paper we give a proof of convergence of a new numerical method introduced in n besse and e sonnendrucker j comput phys 191 2003 pp 341 376 for the vlasov equation the numerical method is based on the semi lagrangian principle and the transport of the gradient of the statistical distribution function in order to get a high order and stable reconstruction these kinds of new schemes have been successfully implemented on unstructured meshes of four dimensional phase space cf n besse etude mathematique et numerique de l equation de vlasov sur des maillages non structures de l espace des phases these de l universite louis pasteur strasbourg france 2003 n besse j segre and e sonnendrucker transport theory statist phys 34 2005 pp 311 332 in order to make a rigorous proof of convergence of this method and simplify the convergence analysis we have considered the periodic one dimensional vlasov poisson system in phase space on a grid the distribution f t x v and the electric field are shown to converge to the exact solution values in h 1 norm the rate of convergence is of mathcal o delta t 2 frac delta x 4 alpha delta t frac delta v 4 alpha delta t alpha in n 2 alpha leq 1

stochastic win stay lose shift strategy with dynamic aspirations in evolutionary social dilemmas in times of plenty expectations rise just as in times of crisis they fall this can be mathematically described as a win stay lose shift strategy with dynamic aspiration levels where individuals aspire to be as wealthy as their average neighbor here we investigate this model in the realm of evolutionary social dilemmas on the square lattice and scale free networks by using the master equation and monte carlo simulations we find that cooperators coexist with defectors in the whole phase diagram even at high temptations to defect we study the microscopic mechanism that is responsible for the striking persistence of cooperative behavior and find that cooperation spreads through second order neighbors rather than by means of network reciprocity that dominates in imitation based models for the square lattice the master equation can be solved analytically in the large temperature limit of the fermi function while for other cases the resulting differential equations must be solved numerically either way we find good qualitative agreement with the monte carlo simulation results our analysis also reveals that the evolutionary outcomes are to a large degree independent of the network topology including the number of neighbors that are considered for payoff determination on lattices which further corroborates the local character of the microscopic dynamics unlike large scale spatial patterns that typically emerge due to network reciprocity here local checkerboard like patterns remain virtually unaffected by differences in the macroscopic properties of the interaction network

adaptive multiresolution semi lagrangian discontinuous galerkin methods for the vlasov equations we develop adaptive numerical schemes for the vlasov equation by combining discontinuous galerkin discretisation multiresolution analysis and semi lagrangian time integration we implement a tree based structure in order to achieve adaptivity both multi wavelets and discontinuous galerkin rely on a local polynomial basis the schemes are tested and validated using vlasov poisson equations for plasma physics and astrophysics

on the relationship between semi lagrangian and lagrange galerkin schemes following a previous result stating their equivalence under constant advection speed semi lagrangian and lagrange galerkin schemes are compared in this paper in the situation of variable coefficient advection equations once known that semi lagrangian schemes can be proved to be equivalent to area weighted lagrange galerkin schemes via a suitable definition of the basis functions we will further prove that area weighted lagrange galerkin schemes represent a small more precisely an o delta t perturbation of exact lagrange galerkin schemes this equivalence implies a general result of stability for semi lagrangian schemes

analysis of a class of quasi monotone and conservative semi lagrangian advection schemes we analyze in the l infty norm a class of semi lagrangian advective schemes introduced by the author and a staniforth in 1992 to improve the solution produced by numerical models for weather prediction and climate studies that use semi lagrangian advective schemes the new quasi monotone and conservative semi lagrangian schemes are l infty stable and converge optimally when the solution is sufficiently smooth

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

networking effects on evolutionary snowdrift game in networks with fixed degrees abstract we study the effects of spatial structures other than the degree distribution on the extent of the emergence of cooperation in an evolutionary snowdrift game by swapping the links in three different types of regular lattices with a fixed degree k we study how the frequency of cooperator f c changes as the clustering coefficient cc which signifies how the nearest neighbors of a vertex are connected and the sharing coefficient sc which signifies how the next nearest neighbors of a vertex are shared by the nearest neighbors are varied for small k a non vanishing cc tends to suppress f c a non vanishing sc also leads to a suppressed f c for the networks studied as the degree increases the sensitivity of f c to the network properties is found to become increasingly weak the result is discussed within the context of the ranking patterns of average payoffs as k changes an approximation for f c which is based on the idea of a finite fully connected network and gives results in good agreement with numerical results is derived in the limit of large k

convergence of an adaptive semi lagrangian scheme for the vlasov poisson system an adaptive semi lagrangian scheme for solving the cauchy problem associated to the periodic 1 1 dimensional vlasov poisson system in the two dimensional phase space is proposed and analyzed a key feature of our method is the accurate evolution of the adaptive mesh from one time step to the next one based on a rigorous analysis of the local regularity and how it gets transported by the numerical flow the accuracy of the scheme is monitored by a prescribed tolerance parameter e which represents the local interpolation error at each time step in the l metric the numerical solutions are proved to converge in l towards the exact ones as e and t tend to zero provided the initial data is lipschitz and has a finite total curvature or in other words that it belongs to w 1 infty cap w 2 1 the rate of convergence is mathcal o delta t 2 varepsilon delta t which should be compared to the results of besse who recently established in siam j numer anal 42 1 350 382 2004 similar rates for a uniform semi lagrangian scheme but requiring that the initial data are in mathcal c 2 several numerical tests illustrate the effectiveness of our approach for generating the optimal adaptive discretizations

convergence analysis of a discontinuous galerkin strang splitting approximation for the vlasov poisson equations a rigorous convergence analysis of the strang splitting algorithm with a discontinuous galerkin approximation in space for the vlasov poisson equations is provided it is shown that under suitable assumptions the error is of order mathcal o tau 2 h q h q tau where tau is the size of a time step h is the cell size and q the order of the discontinuous galerkin approximation in order to investigate the recurrence phenomena for approximations of higher order as well as to compare the algorithm with numerical results already available in the literature a number of numerical simulations are performed

n th order operator splitting schemes and nonreversible systems this paper is concerned with partitioned nth order accurate split operator schemes built using m distinct solution operators for semidiscrete equations of the form frac d dt u j f j 1 u k cdots f j m u k which arise among others from constant coefficient parabolic partial differential equations we prove that for every n geq 3 and m geqslant 2 each solution operator must be applied for at least one backward fractional time step during each complete time step this result has important consequences for applications to the complex ginzburg landau equation with periodic boundary conditions and other partial differential equations with both reversible and nonreversible components furthermore for the special case of n 3 and m 2 we analytically determine all possible schemes

a technique for approximate solutions to schrodinger like equations in the present paper the schro dinger like equations are solved easily quickly and elegantly using adomian s decomposition method the technique has been illustrated by some examples which are of physical interest

evolutionary prisoner s dilemma game on barabasi albert scale free networks an evolutionary prisoner s dilemma game pdg with players located on barabasi albert scale free networks basfn with average connectivity 8 is studied in detail the players are pure strategists and can adopt two strategies either defect or cooperate several alternative update rules determining the evolution of each player s strategy are considered using monte carlo mc simulations we implemented both synchronous and asynchronous update dynamics to calculate the average density of cooperators pc as a function of the temptation to defect b in the equilibrium state for the sake of comparison evolution of cooperative behavior on random regular graphs rrg and regular lattices rl with the same total size and average connectivity as basfn are also investigated we find the overall result that cooperation is sometimes inhibited and sometimes enhanced on the basfn with respect to the cases on the rrg and rl the differences depend on the detailed evaluation function of the players success average payoffs of the players in the present case the different update rules that determine a player s future strategy the synchronous and asynchronous events of strategy updating and also on the temptation to defect c 2007 elsevier b v all rights reserved

convergence of a semi lagrangian scheme for the reduced vlasov maxwell system for laser plasma interaction the subject matter of this paper concerns the numerical approximation of reduced vlasov maxwell models by semi lagrangian schemes such reduced systems have been introduced recently in the literature for studying the laser plasma interaction we recall the main existence and uniqueness results on these topics we present the semi lagrangian scheme and finally we establish the convergence of this scheme

evolutionary mixed games in structured populations cooperation and the benefits of heterogeneity evolutionary games on networks traditionally involve the same game at each interaction here we depart from this assumption by considering mixed games where the game played at each interaction is drawn uniformly at random from a set of two different games while in well mixed populations the random mixture of the two games is always equivalent to the average single game in structured populations this is not always the case we show that the outcome is in fact strongly dependent on the distance of separation of the two games in the parameter space effectively this distance introduces payoff heterogeneity and the average game is returned only if the heterogeneity is small for higher levels of heterogeneity the distance to the average game grows which often involves the promotion of cooperation the presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin and they also emphasize the importance of the population structure in amplifying facilitators of cooperation

convergence of classes of high order semi lagrangian schemes for the vlasov poisson system abstract in this paper we present some classes of high order semi lagran gian schemes for solving the periodic one dimensional vlasov poisson system in phase space on uniform grids we prove that the distribution function f t x v and the electric field e t x converge in the l 2 norm with a rate of displaystyle mathcal o left delta t 2 h m 1 frac h m 1 delta t right where m is the degree of the polynomial reconstruction and delta t and h are respectively the time and the phase space discretization parameters

near field and far field approximations by the adomian and asymptotic decomposition methods the adomian decomposition method and the asymptotic decomposition method give the near field approximate solution and far field approximate solution respectively for linear and nonlinear differential equations the pade approximants give solution continuation of series solutions but the continuation is usually effective only on some finite domain and it can not always give the asymptotic behavior as the independent variables approach infinity we investigate the global approximate solution by matching the near field approximation derived from the adomian decomposition method with the far field approximation derived from the asymptotic decomposition method for linear and nonlinear differential equations for several examples we find that there exists an overlap between the near field approximation and the far field approximation so we can match them to obtain a global approximate solution for other nonlinear examples where the series solution from the adomian decomposition method has a finite convergent domain we can match the pade approximant of the near field approximation with the far field approximation to obtain a global approximate solution representing the true entire solution over an infinite domain

emergence of cooperation among interacting individuals we study the evolution of interacting individuals located on the sites of a regular lattice the individuals play a two action game in which the players either cooperate or defect with respect to a certain issue the main rule of the game is that a player does not change his action when he and his opponent have held the same action in the previous round numerical simulations performed on a square lattice show a stationary state in which the lattice has a finite number of cooperators and defectors and two frozen states one full of cooperators and the other full of defectors

towards effective payoffs in the prisoner s dilemma game on scale free networks we study the transition towards effective payoffs in the prisoner s dilemma game on scale free networks by introducing a normalization parameter guiding the system from accumulated payoffs to payoffs normalized with the connectivity of each agent we show that during this transition the heterogeneity based ability of scale free networks to facilitate cooperative behavior deteriorates continuously eventually collapsing with the results obtained on regular graphs the strategy donations and adaptation probabilities of agents with different connectivities are studied results reveal that strategies generally spread from agents with larger towards agents with smaller degree however this strategy adoption flow reverses sharply in the fully normalized payoff limit surprisingly cooperators occupy the hubs even if the averaged cooperation level due to partly normalized payoffs is moderate

strategy updating depending on local environment enhances cooperation in prisoners dilemma game a new method of strategy updating is proposed in the prisoners dilemma game some players apply the replicator dynamic rule for strategy updating while the others utilize the comprehensive method the intelligent players would consider not only the neighbors payoff but also its environment the results indicate that with the increase of intelligent players the fraction of cooperation increases an evolutionary prisoners dilemma game is studied on a square lattice when local environment is considered and a new strategy updating rule is utilized in this game first individuals are classified as two classes stochastic players and intelligent players the stochastic players are the ones who adopt the rule of replicator dynamics to update strategies and the intelligent players are those who make a decision through comprehensive considerations of the local environment namely the information of different strategy neighbors environment second the intelligent players evaluation is calculated from payoffs and local environment by dempstershafer theory the results indicate that the new strategy updating method promotes cooperation when intelligent individuals utilize the information of different strategy neighborhoods moreover the increasing number of intelligent player promotes cooperation level furthermore it is noteworthy that cooperators will finally coexist with defectors no matter what the proportion of intelligence is which is worthy to think about