on the wave front solution of a competition diffusion system in population dynamics abstract in this paper we consider a competition diffusion system of two equations zhou and pao asymptotic behavior of a competition diffusion system in population dynamics nonlinear anal 6 11 1982 1163 1184 the diffusion coefficients of the system are not equal we prove existence of a wave front solution which connects two nonzero restpoints of the system in the proof we rely essentially on the results of kolmogorov et al a study of diffusion with increase in the quantity of matter and its application to a biological problem bull moscow state univ 17 1937 1 72 we also estimate the wave speed

stable coexistence states in the volterra lotka competition model with diffusion we study the existence uniqueness and stability of coexistence states in the lotka volterra model with diffusion for two competing species we assume that the parameters describing the interactio

global asymptotic stability of 3 species lotka volterra models with diffusion and time delays abstract this paper is concerned with three 3 species time delayed lotka volterra reaction diffusion models with homogeneous neumann boundary condition some simple conditions are obtained for the global asymptotic stability of the nonnegative semitrivial constant steady state solutions these conditions are explicit and easily verifiable and they involve only the reaction rate constants and are independent of the diffusion and time delays the result of global asymptotic stability not only implies the nonexistence of positive steady state solution but also gives some extinction results of the models in the ecological sense the instability of some nonnegative semitrivial constant steady state solutions is also shown the conclusions for the reaction diffusion systems are directly applicable to the corresponding ordinary differential systems

travelling wave and global attractivity in a competition diffusion system with nonlocal delays in this paper we are concerned with a two competition model described by a reaction diffusion system with nonlocal delays which account for the drift of individuals to their present position from their possible positions at previous times by using the iterative technique recently developed in wang et al 2006 14 the sufficient conditions are established for the existence of travelling wave solutions connecting the semi trivial steady state to the coexistence steady state of the considered system when the domain is bounded we investigate the global attractivity of the coexistence steady state of the system under homogeneous neumann boundary conditions as well the approach used is the upper lower solutions and monotone iteration technique

convergence in almost periodic competition diffusion systems the paper deals with the convergence of positive solutions for almost periodic competition diffusion systems the asymptotic almost periodicity of a positive solution for such a system is described by the almost periodicity of the limit set of the corresponding positive motion in the associated skew product flow in the framework of the skew product flow it will be proved that the limit set of any spatially homogeneous positive motion contains at most two minimal sets which are both almost automorphic it will also be proved that if each spatially homogeneous positive solution is asymptotically almost periodic and each spatially homogeneous positive almost periodic solution is lower upper asymptotically lyapunov stable then every positive solution converges to a spatially homogeneous almost periodic solution several important special cases are described where every positive solution converges to a spatially homogeneous almost periodic solution

on the uniqueness of the positive steady state for lotka volterra models with diffusion abstract we give criteria for the uniqueness and stability of the componentwise positive steady state for the diffusive lotka volterra model of several competing species under dirichlet boundary conditions thereby extending known results for cases of only two species in the case of an underlying spatial domain which is one dimensional interval we obtain an estimate for a quantity occurring in the hypotheses of a number of uniqueness results the estimate sharpens those results and gives a partial negative answer to a conjecture of korman and leung

a new approach toward stabilization in a two species chemotaxis model with logistic source abstract this paper aims at providing an alternative approach to study global dynamic properties for a two species chemotaxis model with the main novelty being that both populations mutually compete with the other on account of the lotka volterra dynamics more precisely we consider the following neumann initial boundary value problem u t d 1 u 1 u w 1 u 1 u a 1 v x t 0 v t d 2 v 2 v w 2 v 1 a 2 u v x t 0 0 d 3 w w u v x t 0 in a bounded domain r n n 1 with smooth boundary where d 1 d 2 d 3 1 2 1 2 a 1 a 2 are positive constants when a 1 0 1 and a 2 0 1 it is shown that under some explicit largeness assumptions on the logistic growth coefficients 1 and 2 the corresponding neumann initial boundary value problem possesses a unique global bounded solution which moreover approaches a unique positive homogeneous steady state u v w of above system in the large time limit the respective decay rate of this convergence is shown to be exponential when a 1 1 and a 2 0 1 if 2 is suitable large for all sufficiently regular nonnegative initial data u 0 and v 0 with u 0 0 and v 0 0 the globally bounded solution of above system will stabilize toward 0 1 1 as t in algebraic

global asymptotic stability of lotka volterra 3 species reaction diffusion systems with time delays abstract this paper is concerned with three 3 species time delayed lotka volterra reaction diffusion systems and their corresponding ordinary differential systems without diffusion the time delays may be discrete or continuous and the boundary conditions for the reaction diffusion systems are of neumann type the goal of the paper is to obtain some simple and easily verifiable conditions for the existence and global asymptotic stability of a positive steady state solution for each of the three model problems these conditions involve only the reaction rate constants and are independent of the diffusion effect and time delays the result of global asymptotic stability implies that each of the three model systems coexists is permanent and the trivial and all semitrivial solutions are unstable our approach to the problem is based on the method of upper and lower solutions for a more general reaction diffusion system which gives a common framework for the 3 species model problems some global stability results for the 2 species competition and prey predator reaction diffusion systems are included in the discussion

on nonlinear reaction diffusion systems abstract this paper presents a qualitative analysis for a coupled system of two reaction diffusion equations under various boundary conditions which arises from a number of physical problems the nonlinear reaction functions are classified into three basic types according to their relative quasi monotone property for each type of reaction functions an existence comparison theorem in terms of upper and lower solutions is established for the time dependent system as well as some boundary value problems three concrete physical systems arising from epidemics biochemistry and engineering are taken as representatives of the basic types of reacting problems through suitable construction of upper and lower solutions various qualitative properties of the solution for each system are obtained these include the existence and bounds of time dependent solutions asymptotic behavior of the solution stability and instability of nontrivial steady state solutions estimates of stability regions and finally the blowing up property of the solution special attention is given to the homogeneous neumann boundary condition

numerical solutions for some coupled systems of nonlinear boundary value problems in the well known volterra lotka model concerning two competing species with diffusion the densities of the species are governed by a coupled system of reaction diffusion equations the aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems this iterative scheme is based on the method of upper lower solutions which leads to two monotone sequences from some uncoupled linear systems it is shown that each of the two sequences converges to a nontrivial solution of the discrete equations the model under consideration may have one two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration numerical results are given for these solutions under both the dirichlet boundary condition and the mixed type boundary condition

instability of equilibria in some delay reaction diffusion systems a new result is derived which extends a known instability result for a class of reaction diffusion equations to a corresponding system incorporating time delay effects for a significant class of nonlinear equations it is shown that an unstable equilibrium solution of the reaction diffusion system cannot be stabilised by the introduction of delay the result is applied to problems posed on convex domains with homogeneous neumann boundary conditions finally global methods in bifurcation theory are applied to a delay reaction diffusion system of lotka volterra type representing the interaction of two mobile species the existence of a countable set of continua consisting of unstable equilibrium solutions for this system is proved

the formation of topographic maps that maximize the average mutual information of the output responses to noiseless input signals this article introduces an extremely simple and local learning rule for to pographic map formation the rule called the maximum entropy learning rule mer maximizes the unconditional entropy of the map s output for any type of input distribution the aim of this article is to show that mer is a viable strategy for building topographic maps that maximize the average mutual information of the output responses to noiseless input signals when only input noise and noise added input signals are available

global dynamics of the lotka volterra competition diffusion system diffusion and spatial heterogeneity i in the first part of this series of three papers we investigate the combined effects of diffusion spatial variation and competition ability on the global dynamics of a classical lotka volterra competition diffusion system we establish the main results that determine the global asymptotic stability of semitrivial as well as coexistence steady states hence a complete understanding of the change in dynamics is obtained immediately our results indicate confirm that when spatial heterogeneity is included in the model diffusion driven exclusion could take place when the diffusion rates and competition coefficients of both species are chosen appropriately 2015 wiley periodicals inc

solutions to arithmetic differential equations in algebraically closed fields abstract arithmetic differential equations or geometry exploits analogies between derivations and p derivations arising from lifts of frobenius to study problems in arithmetic geometry along the way two main classes such functions describable as series arose prominently namely characters of abelian schemes and isogeny covariant modular forms however the theory of these functions is not as straightforward in ramified settings overconvergence was introduced in 13 to account for these issues which essentially imposes growth conditions extensions of these series to a fixed level of ramification necessary as such extensions have non trivial fractional coefficients in this article we introduce a rescaling process which identifies a class of functions we call totally overconvergent which extend all the way to the algebraic closure of ring of integers of the maximally unramified extension of q p applications built on these functions allow one to remove boundedness assumptions on ramification the bulk of the article is devoted to establishing that most functions arising in practice namely those in the applications described in 5 7 8 are totally overconvergent which essentially extends results in 13 to unbounded ramification

asymptotic behaviour of solutions of periodic competition diffusion system on considere le systeme d equations de reaction diffusion u t k 1 u a bu cv v t k 2 v v d eu fv ou k 1 k 2 a b f sont des fonctions suffisamment lisses definies sur un cylindre ou est un domaine borne lisse de r n

dynamics of lotka volterra competition reaction diffusion systems with degenerate diffusion abstract this paper is dealt with a class of lotka volterra competition reaction diffusion system and a competitor competitor mutualist system with density dependent diffusion in a bounded domain under the three basic types of dirichlet neumann and robin boundary conditions the governing equations for the competition system consist of an arbitrary number of degenerate quasilinear parabolic equations while the competitor competitor mutualist system involves three degenerate equations the goal of the paper is to show the existence of positive steady state solutions or quasi solutions the existence and uniqueness of a classical global time dependent solution and the asymptotic behavior of the time dependent solution in relation to the steady state solutions or quasi solutions the above goals are achieved under a very simple condition on the reaction rates of the reaction functions and these results yield a global attractor and the coexistence of the competing species in the case of neumann boundary condition the system has a unique constant positive steady state solution which is a global attractor of all the competing species the above conclusions lead to some interesting distinct dynamic behavior between degenerate quasilinear reaction diffusion systems and the corresponding semilinear reaction diffusion systems in which some or all of the competing species may be in extinction

nonlinear impulse evolution systems and applications to population models abstract we apply results on the existence uniqueness and stability of solutions obtained previously for the abstract impulse evolution system to the study of the mathematical model of population subject to abrupt changes of important biological parameters caused by harvesting diseases immigration etc

traveling waves and competitive exclusion in models of resource competition and mating interference abstract in this article we study reaction diffusion models for two closed related biological species u and v under resource competition and mating interference from v species to u species the effect of one sided sexual competition makes the trivial state and u dominance state both unstable while the v dominance state is shown to be asymptotically stable with attraction regions and convergent rates depending on the biological parameters using the upper lower solution method we further prove that for a family of wave speeds there exist traveling wave solutions connecting the u dominance state and the v dominance state at this confirms an earlier conjecture that unbalanced mating interference will lead to competitive exclusion these results can also be obtained on an extended model with instantaneous effects of resource competition and temporal delay on mating interference through a transformation into three equation system we prove that the temporal delay does not affect the stability of the steady states and the existence of the traveling waves but causes changes on the attraction regions and convergence rates finally numerical simulations are also presented to illustrate the theoretical results

coexistence and stability of a competition diffusion system in population dynamics abstract the coexistence and stability of the population densities of two competing species in a bounded habitat are investigated in the present paper where the effect of dispersion transportation is taken into consideration the mathematical problem involves a coupled system of lotka volterra type reaction diffusion equations together with some initial and boundary conditions including the dirichlet neumann and third type necessary and sufficient conditions for the coexistence and competitive exclusion are established and the effect of diffusion is explicitly given for the stability problem general criteria for the stability and instability of a steady state solution are established and then applied to various situations depending on the relative magnitude among the physical parameters also given are necessary and sufficient conditions for the existence of multiple steady state solutions and the stability or instability of each of these solutions special attention is given to the neumann boundary condition with respect to which some threshold results for the coexistence and stability or instability of the four uniform steady states are characterized it is shown in this situation that only one of the four constant steady states is asymptotically stable while the remaining three are unstable the stability or instability of these states depends solely on the relative magnitude among the various rate constants and is independent of the diffusion coefficients