evolutionary minority game with heterogeneous strategy distribution abstract we present detailed numerical results for a modified form of the so called minority game which provides a simplified model of a competitive market each agent has a limited set of strategies and competes to be in a minority an evolutionary rule for strategy modification is included to mimic simple learning the results can be understood by considering crowd formation within the population

point wise error estimate of a conservative difference scheme for the fractional schrodinger equation in this paper a new conservative difference scheme is proposed for solving the nonlinear space fractional schrodinger equation the riesz space fractional derivative is approximated by the second order accurate weighted and shifted grunwald difference operator building on a careful analysis of this operator the conservation properties including the mass and energy are analyzed and some norm equivalences are established then the numerical solution is shown to be bounded in various norms uniformly with respect to the discretization parameters and optimal order bounds on the global error of the scheme in the l 2 norm semi h 2 norm and l norm are derived the uniform bounds on the numerical solutions as well as the error bounds hold unconditionally in the sense that no restriction on the size of the time step in terms of the spatial mesh size needs to be assumed numerical tests are performed to support our theoretical results

approximate controllability of fractional stochastic differential equations driven by mixed fractional brownian motion via resolvent operators abstractin this manuscript we investigate the approximate controllability of a class of fractional stochastic differential equations driven by mixed fractional brownian motion in hilbert space with hurst parameter h 12 1 the main results are obtained by employing fractional calculus analytic resolvent operators and with the help of schaefer s fixed point theorem under the assumption that the corresponding linear system is approximately controllable finally in order to validate the obtained theoretical results an illustrative example is provided

survival probabilities in time dependent random walks we analyze the dynamics of random walks in which the jumping probabilities are periodic time dependent functions in particular we determine the survival probability of biased walkers who are drifted towards an absorbing boundary the typical lifetime of the walkers is found to decrease with an increment in the oscillation amplitude of the jumping probabilities we discuss the applicability of the results in the context of complex adaptive systems

composition of pseudo almost automorphic and asymptotically almost automorphic functions this paper is concerned with pseudo almost automorphic functions which are more general and complicated than pseudo almost periodic functions and asymptotically almost automorphic functions new results concerning the composition of pseudo almost automorphic functions are established

an energy conservative difference scheme for the nonlinear fractional schrodinger equations abstract in this paper an energy conservative crank nicolson difference scheme for nonlinear riesz space fractional schrodinger equations is studied we give a rigorous analysis of the conservation properties including mass conservation and energy conservation in the discrete sense based on brouwer fixed point theorem the existence of the difference solution is proved by virtue of the energy method the difference solution is shown to be unique and convergent at the order of o 2 h 2 in the l 2 norm with time step and mesh size h finally a linearized iterative algorithm is presented and numerical experiments are given to confirm the theoretical results

weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations this paper is concerned with the existence and uniqueness of a weighted pseudo almost automorphic mild solution to the semilinear fractional equation d t au t au t d t a 1f t u t t r 1 a 2 in complex banach spaces with s p weighted pseudo almost automorphic coefficients where a is a linear densely defined operator of sectorial type on a complex banach space x moreover we present an application to a fractional wave equation

an implicit midpoint difference scheme for the fractional ginzburg landau equation this paper proposes and analyzes an efficient difference scheme for the nonlinear complex ginzburg landau equation involving fractional laplacian the scheme is based on the implicit midpoint rule for the temporal discretization and a weighted and shifted grunwald difference operator for the spatial fractional laplacian by virtue of a careful analysis of the difference operator some useful inequalities with respect to suitable fractional sobolev norms are established then the numerical solution is shown to be bounded and convergent in the l h 2 norm with the optimal order o 2 h 2 with time step and mesh size h the a priori bound as well as the convergence order holds unconditionally in the sense that no restriction on the time step in terms of the mesh size h needs to be assumed numerical tests are performed to validate the theoretical results and effectiveness of the scheme

minority game with peer pressure abstract to study the interplay between global market choice and local peer pressure we construct a minority game like econophysical model in this so called networked minority game model every selfish player uses both the historical minority choice of the population and the historical choice of one s neighbors in an unbiased manner to make decision results of numerical simulation show that the level of cooperation in the networked minority game differs remarkably from the original minority game as well as the prediction of the crowd anticrowd theory we argue that the deviation from the crowd anticrowd theory is due to the negligence of the effect of a four point correlation function in the effective hamiltonian of the system

faedo galerkin approximate solutions of a neutral stochastic fractional differential equation with finite delay abstract in this work we study a class of neutral stochastic fractional differential equation in an arbitrary separable hilbert space h we obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by projection of considered associated integral equation onto finite dimensional space the existence and uniqueness of solutions to every approximate integral equation are obtained by using banach fixed point theorems and analytic semigroup theory we show the convergence of the solutions by using faedo galerkin approximations and give an example to show the effectiveness of the main theory finally we provide the conclusion at the end

on the minority game analytical and numerical studies abstract we investigate further several properties of the minority game we have recently introduced we explain the origin of the phase transition and give an analytical expression of 2 n in the n 2 m region the ability of the players to learn a given payoff is also analyzed and we show that the darwinian evolution process tends to a self organized state in particular the lifetime distribution is a power law with exponent 2 furthermore we study the influence of identical players on their gain and on the systems performance finally we show that large brains always take advantage of small brains

the optimal control of a new class of impulsive stochastic neutral evolution integro differential equations with infinite delay abstractin this paper we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in hilbert spaces first by using stochastic analysis the analytic semigroup theory fractional powers of closed operators and suitable fixed point theorems we prove an existence result of mild solutions for the control systems in the norm without the assumptions of compactness next we derive the existence conditions of optimal pairs of these systems finally application to a nonlinear impulsive stochastic parabolic optimal control system is considered

existence and uniqueness attraction for stochastic age structured population systems with diffusion and poisson jump in this paper the problems about the existence and uniqueness attraction for strong solution of stochastic age structured population systems with diffusion and poisson jump are considered under the non lipschitz condition with the lipschitz condition being considered as a special case the existence and uniqueness for such systems is firstly proved by using the burkholder davis gundy inequality b d g inequality and ito s formula and then by using a novel inequality technique some sufficient conditions ensuring the existence for the domain of attraction are established as another by product the exponential stability in mean square moment of strong solution for such systems can be also discussed

the hamming distance in the minority game abstract we investigate different versions of the minority game a toy model for agents buying and selling a commodity the hamming distance between the strategies used by agents to make decisions is introduced as an analytical tool to determine several properties of these models the success rate of the agents in an adaptive version of the game is compared with the rate from a stochastic version it is shown numerically and analytically that the adaptive process is inefficient increasing the success rate of the unused strategies while decreasing the success rate of the strategies used by the agents the agents do not do as well as if they were forced to use only one strategy permanently a version of the game in which the agents strategies evolve is also analysed using the notion of distance the agents evolve into a state in which they are all using one strategy which is again the state that yields the maximum success rate

existence of almost automorphic mild solutions to non autonomous neutral stochastic differential equations abstract in this paper we consider the existence and uniqueness of square mean and weighted pseudo almost automorphic mild solutions to a class of nonautonomous stochastic neutral differential equations with infinite delay in real separable hilbert spaces a new set of sufficient conditions are established for obtaining the required result to prove the main result we use banach contraction principle together with evolution family of operators some known results are generalized and improved an application to the stochastic nonlinear heat equation with infinite delay is provided to illustrate the obtained theory

on some fractional evolution equations abstract in this paper the solutions of some evolution equations with fractional orders in a banach space are considered conditions are given which ensure the existence of a resolvent operator for an evolution equation in a banach space

finite difference approximations for fractional advection dispersion flow equations fractional advection dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium in this paper we develop practical numerical methods to solve one dimensional fractional advection dispersion equations with variable coefficients on a finite domain the practical application of these results is illustrated by modeling a radial flow problem use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site

on some fractional stochastic delay differential equations abstract we consider the cauchy problem for an abstract stochastic delay differential equation driven by fractional brownian motion with the hurst parameter h 1 2 we prove the existence and uniqueness for this problem when the coefficients have enough regularity the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of any order we prove the theorem by using the convergence of the picard lindel o f iterations in l 2 to a solution of this problem which admits a smooth density with respect to lebesgue s measure on r

almost automorphic and pseudo almost automorphic mild solutions to an abstract differential equation in banach spaces in this paper we prove some existence results for almost automorphic and pseudo almost automorphic mild solutions to a class of abstract differential equations in banach spaces the main technique is based on some composition theorems combined with the contraction mapping theorem finally we present an application to a semilinear partial differential equation with dirichlet conditions

the full strategy minority game abstract the full strategy minority game f s m g is an instance of the minority game m g which includes a single copy of every potential agent in this work we explicitly solve the f s m g thanks to certain symmetries of this game furthermore by considering the m g as a statistical sample of the f s m g we compute approximated values of the key variable 2 n in the symmetric phase for different versions of the m g as another application we prove that our results can be easily modified in order to handle certain kinds of initial biased strategy scores in particular when the bias is introduced at the agents level we also show that the f s m g verifies a strict period two dynamics i e period two dynamics satisfied with probability 1 giving to the best of our knowledge the first example of an instance of the m g for which this feature can be analytically proved thanks to this property it is possible to compute in a simple way the probability that a general instance of the m g breaks the period two dynamics for the first time in a given simulation

existence uniqueness and stability of stochastic neutral functional differential equations of sobolev type in this paper we are mainly concerned with a class of stochastic neutral functional differential equations of sobolev type with poisson jumps under two different sets of conditions we establish the existence of the mild solution by applying the leray schauder alternative theory and the sadakovskii s fixed point theorem respectively furthermore we use the bihari s inequality to prove the osgood type uniqueness also the mean square exponential stability is investigated by applying the gronwall inequality finally two examples are given to illustrate the theory results

el farol revisited this article is concerned with the global behavior of agents in the el farol bar problem in particular we discuss global attendance in terms of its mean and variance and show that there is a strong dependence of both on the externally imposed comfort level we present a possible interpretation for the observed behavior and propose that the mean attendance converges to the perceived threshold value as opposed to the actually imposed one

time dependent random walks and the theory of complex adaptive systems motivated by novel results in the theory of complex adaptive systems we analyze the dynamics of random walks in which the jumping probabilities are time dependent we determine the survival probability in the presence of an absorbing boundary for an unbiased walk the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities on the other hand a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability we use the results to reveal the underlying dynamics responsible for the phenomenon of self segregation and clustering observed in the evolutionary minority game

crank nicolson difference scheme for the coupled nonlinear schrodinger equations with the riesz space fractional derivative in this paper the crank nicolson cn difference scheme for the coupled nonlinear schrodinger equations with the riesz space fractional derivative is studied the existence of this difference solution is proved by the brouwer fixed point theorem the stability and convergence of the cn scheme are discussed in the l 2 norm when the fractional order is two all those results are in accord with the difference scheme developed for the classical non fractional coupled nonlinear schrodinger equations some numerical examples are also presented

effects of dynamic response time in an evolving market abstract considering the time scales of global information and personal reaction we study the role of dynamic response time in the evolution of collective behavior in an evolving market the insensitiveness to the market information makes the population cluster around a kind of extreme behavior in which they always follow what happened last time while a sensitive population tends to self segregate into opposing groups the average success rate r among all the agents is found to have a nonmonotonic dependence on the time scale parameter q there exists a critical value below above which r decreases increases with the rise of q theoretical analyses demonstrate that the higher efficiency found in the market with an insensitive population is related to its predictability in such a predictable market the agents following current prediction have a higher winning probability than those rejecting it analytical calculations are in good agreement with numerical data

a linearly implicit conservative difference scheme for the space fractional coupled nonlinear schrodinger equations abstract in this paper a linearly implicit conservative difference scheme for the coupled nonlinear schrodinger equations with space fractional derivative is proposed this scheme conserves the mass and energy in the discrete level and only needs to solve a linear system at each step the existence and uniqueness of the difference solution are proved the stability and convergence of the scheme are discussed and it is shown to be convergent of order o 2 h 2 in the discrete l 2 norm with the time step and mesh size h when the fractional order is two all those results are in accord with the difference scheme proposed for the classical non fractional coupled nonlinear schrodinger equations some numerical examples are also reported

effects of imitation in a competing and evolving population abstract we propose and study a modified version of the evolutionary minority game consisting of a competing population agents in the population are repeatedly competing to be in a minority and they have a common strategy each agent has a parameter p characterizing the probability that she is following the prediction of the common strategy agents are lined up in a one dimensional chain with periodic boundary condition imitation is allowed among nearest neighboring agents numerical results show that the agents evolve into a state in which they self segregate into opposite groups characterized by extreme behavior and imitation leads to considerable enhancement in the overall performance of the population

some properties of pseudo almost automorphic functions and applications to abstract differential equations abstract this paper is concerned with some properties of pseudo almost automorphic functions which are more general and complicated than pseudo almost periodic functions using these properties we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a banach space

fractional ginzburg landau equation for fractal media abstract we derive the fractional generalization of the ginzburg landau equation from the variational euler lagrange equation for fractal media to describe fractal media we use the fractional integrals considered as approximations of integrals on fractals some simple solutions of the ginzburg landau equation for fractal media are considered and different forms of the fractional ginzburg landau equation or nonlinear schrodinger equation with fractional derivatives are presented the agrawal variational principle and its generalization have been applied

a note on exponential stability for impulsive neutral stochastic partial functional differential equations in this note the problem on the exponential stability in mean square moment of mild solution to impulsive neutral stochastic partial functional differential equations is considered by employing the inequality technique some sufficient conditions are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained result

existence results for an impulsive neutral stochastic fractional integro differential equation with infinite delay abstract in this work we consider an impulsive neutral stochastic fractional integro differential equation with infinite delays in an arbitrary separable hilbert space the existence of mild solution is obtained by using resolvent operator and fixed point theorems an example is considered to illustrate the theory and conclusion is also provided at the end of the manuscript

an efficient split step quasi compact finite difference method for the nonlinear fractional ginzburg landau equations abstract in this paper we propose a split step quasi compact finite difference method to solve the nonlinear fractional ginzburg landau equations both in one and two dimensions the original equations are split into linear and nonlinear subproblems the riesz space fractional derivative is approximated by a fourth order fractional quasi compact method furthermore an alternating direction implicit scheme is constructed for the two dimensional linear subproblem the unconditional stability and convergence of the schemes are proved rigorously in the linear case numerical experiments are performed to confirm our theoretical findings and the efficiency of the proposed method

existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations abstract fractional stochastic differential equations have gained considerable importance due to their application in various fields of science and engineering this paper is concerned with the square mean pseudo almost automorphic solutions for a class of fractional stochastic differential equations in a hilbert space the main objective of this paper is to establish the existence and uniqueness of square mean pseudo almost automorphic mild solutions to a linear and semilinear case of these equations a new set of sufficient conditions is obtained to achieve the required result by using the stochastic analysis theory and fixed point strategy finally an example is provided to illustrate the obtained theory

almost automorphic mild solutions to fractional differential equations abstract we introduce the concept of resolvent families to prove the existence of almost automorphic mild solutions to the differential equation d t u t a u t t n f t 1 2 n z considered in a banach space x where f r x is almost automorphic we also prove the existence and uniqueness of an almost automorphic mild solution of the semilinear equation d t u t a u t f t u t 1 2 assuming f t x is almost automorphic in t for each x x satisfies a global lipschitz condition and takes values on x finally we prove also the existence and uniqueness of an almost automorphic mild solution of the semilinear equation d t u t a u t f t u t u t 1 2 under analogous conditions as in the previous case

on a fractional ginzburg landau equation and 1 2 harmonic maps into spheres this paper is devoted to the asymptotic analysis of a fractional version of the ginzburg landau equation in bounded domains where the laplacian is replaced by an integro differential operator related to the square root laplacian as defined in fourier space in the singular ginzburg landau limit we show that solutions with uniformly bounded energy converge weakly to sphere valued 1 2 harmonic maps i e the fractional analogues of the usual harmonic maps in addition the convergence holds in smooth functions spaces away from a n 1 rectifiable closed set of finite n 1 hausdorff measure the proof relies on the representation of the square root laplacian as a dirichlet to neumann operator in one more dimension and on the analysis of a boundary version of the ginzburg landau equation besides the analysis of the fractional ginzburg landau equation we also give a general partial regularity result for stationary 1 2 harmonic maps in arbitrary dimension

pseudo almost automorphic mild solutions to nonautonomous differential equations and applications abstract in this paper we introduce a new concept of bi almost automorphic functions and obtain new existence and uniqueness theorems for pseudo almost automorphic mild solutions to several nonautonomous differential equations moreover two examples are given to illustrate the general theorems

square mean pseudo almost automorphic process and its application to stochastic evolution equations abstract this paper introduces the concept of the square mean pseudo almost automorphy for a stochastic process also it introduces the properties on the completeness and the composition of the space that consists of such processes with appropriate settings and by virtue of the theory of the semigroups of the operators to an evolution family the banach fixed point theorem and the stochastic analysis techniques this paper investigates the existence the uniqueness and the global stability of the square mean pseudo almost automorphic solutions for a general class of stochastic evolution equations finally this paper provides an illustrative example to justify the practical usefulness of the established theoretical results

dissipation preserving galerkin legendre spectral methods for two dimensional fractional nonlinear wave equations abstract in this paper we consider implicit and linearized dissipation preserving galerkin legendre spectral methods to solve space fractional nonlinear damped wave equation in two dimensions the full discrete schemes preserve dissipation of energy in damped case and conservation of energy in undamped case moreover the stability and convergence analysis of the full discrete schemes are rigorously given furthermore we get that two methods are convergent with second order accuracy in time and optimal error estimates in space in order to reduce the computational cost we adopt matrix diagonalization approach to solve the resulting algebraic systems in numerical implementation numerical results are presented to validate the theoretical analysis

existence and controllability results for stochastic fractional evolution hemivariational inequalities in this paper we study a class of stochastic evolution hemivariational inequalities with fractional derivative the existence of mild solutions and controllability results are obtained by applying fractional calculation stochastic analysis techniques a fixed point theorem of multivalued maps and properties of generalized clarke subdifferential an example is included to show the applicability of our results

statistical properties of the attendance time series in the minority game abstract we study the statistical properties of the attendance time series corresponding to the number of agents making a particular decision in the minority game mg we focus on the analysis of the probability distribution and the autocorrelation function of the attendance over a time interval in the efficient phase of the game in this regime both the probability distribution and the autocorrelation function are shown to have similar behaviour for time differences corresponding to multiples of 2 2m which is twice the number of possible history bit strings in a mg with agents making decisions based on the most recent m outcomes of the game

crowd effects and volatility in markets with competing agents abstract we present analytic and numerical results for two models namely the minority model and the bar attendance model which offer simple paradigms for a competitive marketplace both models feature heterogeneous agents with bounded rationality who act using inductive reasoning we find that the effects of crowding are crucial to the understanding of the macroscopic fluctuations or volatility in the resulting dynamics of these systems

statistical analysis of the evolutionary minority game with different capacities abstract in this paper we consider the evolutionary minority game with different capacities with the increase of capacity level 1 the probability n of room1 with n agents changes from one normal distribution to two normal distributions and back to one normal distribution again when room2 is the basic strategy the probability of room1 with n agents is a small normal distribution and when room1 is the basic strategy the probability of room1 with n agents is a large normal distribution we calculate the integral of the normal distributions and explain the characters in the figures for instance the room with more capacity represents the interest of the majority and the room has more probability to win

a linearized crank nicolson galerkin method for the ginzburg landau model the time dependent ginzburg landau model is used extensively in studying the nonequilibrium state of superconductivity the computer simulation of this model requires high performance computing power and reliable and efficient numerical methods to solve the ginzburg landau equtions in this paper a linearized crank nicolson galerkin method is proposed for solving these nonlinear and coupled partial differential equations the method uses the galerkin finite element approximation in spatial discretization and the crank nicolson implicit scheme in time discretization together with certain techniques which linearize and decouple the ginzburg landau equations while retaining the stabillity and accuracy of the crank nicolson scheme the proposed approach results in symmetric and positive definite matrix problems thus substantially improving the computational efficiency furthermore and even more important the proposed approach is suitable for large scale parallel computation numerical results from simulating the vortex dynamics of superconductivity by using the linearized crank nicolson galerkin method are presented

temporal oscillations and phase transitions in the evolutionary minority game the study of societies of adaptive agents seeking minority status is an active area of research recently it has been demonstrated that such systems display an intriguing phase transition agents tend to self segregate or to cluster according to the value of the prize to fine ratio r we show that such systems do not establish a true stationary distribution the winning probabilities of the agents display temporal oscillations the amplitude and frequency of the oscillations depend on the value of r the temporal oscillations that characterize the system explain the transition in the global behavior from self segregation to clustering in the r 1 case

a fourth order approximation of fractional derivatives with its applications a new fourth order difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted grunwald formulae combining the compact technique the properties of proposed fractional difference quotient operator are presented and proved then the new approximation formula is applied to solve the space fractional diffusion equations by the energy method the proposed quasi compact difference scheme is proved to be unconditionally stable and convergent in l2 norm for both 1d and 2d cases several numerical examples are given to confirm the theoretical results

stochastic fractional evolution equations with fractional brownian motion and infinite delay abstract in this paper we consider a class of stochastic fractional evolution equations with infinite delay and a fractional brownian motion in a hilbert space by the stochastic analysis technique we establish the existence and uniqueness of mild solutions for these equations under non lipschitz condition with lipschitz conditions being considered as a special case an example is provided to illustrate the theory

existence result for fractional neutral stochastic integro differential equations with infinite delay this paper is concerned with the existence of mild solutions for a class of fractional neutral stochastic integro differential equations with infinite delay in hilbert spaces a sufficient condition for the existence is obtained under non lipschitz conditions by means of sadovskii s fixed point theorem an example is given to illustrate the theory

maximum norm error analysis of a difference scheme for the space fractional cnls the difference method for the space fractional coupled nonlinear schrodinger equations cnls is studied the fractional centered difference is used to approximate the space fractional laplacian this scheme conserves the discrete mass and energy due to the nonlocal nature of fractional laplacian in the classic sobolev space it is hard to obtain the error estimation in l to overcome this difficulty the fractional sobolev space h 2 and a fractional norm equivalence in h 2 are introduced then the convergence of order o h 2 2 in l is proved by fractional sobolev inequality where h is the mesh size and is the time step numerical examples are given to illustrate the theoretical results at last

square mean almost automorphic mild solutions to non autonomous stochastic differential equations in hilbert spaces in this paper we first refine the definition of square mean almost automorphic functions introduced in fu and liu 2010 11 then we prove the existence and uniqueness of square mean almost automorphic mild solutions for a class of non autonomous stochastic differential equations in a real separable hilbert space some additional properties of square mean almost automorphic functions are also provided to prove our main result we use the banach contraction mapping principle

a note on exponential stability for second order neutral stochastic partial differential equations with infinite delays in the presence of impulses in this work the problem on the exponential stability for second order neutral stochastic partial differential equations with infinite delays is considered in the presence of impulses under some conditions by employing the new integral inequality technique some algebraic criteria of stability are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained results

split step alternating direction implicit difference scheme for the fractional schrodinger equation in two dimensions in this paper we propose a conservative and effective difference scheme for solving the two dimensional nonlinear space fractional schrodinger equation with the riesz fractional derivative the scheme is constructed by combining the split step method for handling the nonlinearity with the alternating direction implicit adi method for resolving the multi dimensions difficulty the riesz space fractional derivative is approximated by the second order accurate fractional centered difference based on matrix analysis we show that in the discrete sense the scheme conserves the mass and energy for linear problems and conserves the mass for nonlinear problems the unconditional convergence is proved rigorously in the linear case numerical tests are performed to support our theoretical results and show the efficiency of the proposed scheme

almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations abstract in this paper applying the theory of semigroups of operators to evolution family and banach fixed point theorem we prove the existence and uniqueness of an a almost automorphic weighted pseudo almost automorphic mild solution of the semilinear evolution equation x t a t x t f t x t in banach space under conditions

statistical mechanics of systems with heterogeneous agents minority games we study analytically a simple game theoretical model of heterogeneous interacting agents we show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz such a stationary state differs from the nash equilibrium where each agent maximizes her own utility the latter turns out to be characterized by a replica symmetry broken structure numerical results fully agree with our analytical findings

approximate mild solutions of fractional stochastic evolution equations in hilbert spaces in this paper we study the approximate mild solutions of a class of fractional stochastic evolution equations in hilbert spaces by constructing picard type approximate sequences we present the approximate results under the non lipschitz and linear growth conditions

on almost automorphic mild solutions for fractional semilinear initial value problems abstract this paper investigates almost automorphic mild solutions of the fractional semilinear equation d x t a x t f t x t 0 1 considered in a banach space x where a is a linear operator of sectorial type 0 some sufficient conditions are given for the existence uniqueness and uniform stability of almost automorphic mild solutions to this semilinear equation

strategy updating rules and strategy distributions in dynamical multiagent systems in the evolutionary version of the minority game agents update their strategies gene value p in order to improve their performance motivated by the recent intriguing results obtained for prize to fine ratios which are smaller than unity we explore the system s dynamics with a strategy updating rule of the form p p delta p 0 or p or 1 we find that the strategy distribution depends strongly on the values of the prize to fine ratio r the length scale delta p and the type of boundary condition used we show that these parameters determine the amplitude and the frequency of the temporal oscillations observed in the gene space these regular oscillations are shown to be the main factors which determine the strategy distribution of the population in addition we find that the agents characterized by p 1 2 a coin tossing strategy have the best chances of survival at asymptotically long times regardless of the value of delta p and the boundary conditions used

a new composition theorem for square mean almost automorphic functions and applications to stochastic differential equations abstract in this paper we establish a new composition theorem for square mean almost automorphic functions under conditions which are different from lipschitz conditions in the literature we apply this new composition theorem together with schauder s fixed point theorem to investigate the existence of square mean almost automorphic mild solutions for a stochastic differential equation in a real separable hilbert space finally an interesting corollary is also given for the sub linear growth cases

a fourth order compact adi scheme for two dimensional nonlinear space fractional schrodinger equation in this paper a novel compact operator is derived for the approximation of the riesz derivative with order alpha in 1 2 the compact operator is proved with fourth order accuracy combining the compact operator in space discretization a linearized difference scheme is proposed for a two dimensional nonlinear space fractional schrodinger equation it is proved that the difference scheme is uniquely solvable stable and convergent with order o tau 2 h 4 where tau is the time step size h max h 1 h 2 and h 1 h 2 are space grid sizes in the x direction and the y direction respectively based on the linearized difference scheme a compact alternating direction implicit scheme is presented and analyzed numerical results demonstrate that the compact operator does not bring in extra computational cost but improves the accuracy of the scheme greatly

existence of pseudo almost automorphic solutions to some abstract differential equations with sp pseudo almost automorphic coefficients abstract this paper introduces and studies the notion of s p pseudo almost automorphy or stepanov like pseudo almost automorphy which generalizes in a natural fashion the concept of pseudo almost automorphy that was recently introduced in the literature by liang xiao and zhang we next obtain the existence of pseudo almost automorphic solutions to some differential equations with s p pseudo almost automorphic coefficients

theory of the evolutionary minority game we present a theory describing a recently introduced model of an evolving adaptive system in which agents compete to be in the minority the agents themselves are able to evolve their strategies over time in an attempt to improve their performance the theory explicitly demonstrates the self interaction or market impact that agents in such systems experience