asymptotic pattern for a partial neutral functional differential equation abstract in the present article the asymptotic speed of spread and traveling wavefronts of a partial neutral functional differential equation pnfde are investigated a variable transform yields to a partial retarded functional differential equation prfde with infinite number of constant delays the relation between the above pnfde and prfde is studied and an equivalence in a certain meaning of these two equations is verified using this equivalence we in fact obtain the existence and uniqueness of solution for the initial value problem of the pnfde we then consider the truncated system of the above prfde which is a partial retarded functional differential equation with finite number of constant delays we establish the existence of the traveling wave solution and the spreading speed for this truncated system a limit argument and the method of finite delay approximation are used to obtain the existence of the traveling wave solutions and the spreading speed for the prfde with infinite number of constant delays this leads to the existence of the traveling wave solution and the spreading speed for the considered pnfde by the above equivalence at last we confirm that the spreading speed is coincidental with the minimal wave speed for all equations an example is given to illustrate the application of our results

traveling wave solutions in a diffusive system with two preys and one predator abstract this paper is concerned with the traveling wave solutions in a diffusive system with two preys and one predator by constructing upper and lower solutions the existence of nontrivial traveling wave solutions is established the asymptotic behavior of traveling wave solutions is also confirmed by combining the asymptotic spreading with the contracting rectangles applying the theory of asymptotic spreading the nonexistence of traveling wave solutions is proved

on the geometry of wave solutions of a delayed reaction diffusion equation abstract the aim of this paper is to study the existence and the geometry of positive bounded wave solutions to a non local delayed reaction diffusion equation of the monostable type

stability of strong travelling waves for a non local time delayed reaction diffusion equation the paper is concerned with a non local time delayed reaction diffusion equation we prove the time asymptotic stability of a travelling wavefront without a smallness assumption on its wavelength i e the so called strong wavefront by means of the technical weighted energy method when the initial perturbation around the wave is small the exponential convergent rate is also given selection of a suitable weight plays a key role in the proof

traveling waves solutions for partial neutral differential equations abstract using monotonicity techniques and the schauder fixed point theorem we study the existence of traveling waves for neutral partial differential equations in the last section we illustrate our results on the neutral versions of the kpp fisher and the kobayashi equations

traveling wave solutions for gause type predator prey systems with density dependence a heteroclinic orbit in r4 abstract this paper investigates the existence of traveling wave solutions for a class of diffusive gause type predator prey systems with linear density dependence for predator using the shooting method we establish the existence of a non negative traveling wave solution connecting a boundary equilibrium point to the coexistence equilibrium point with the help of topological method of wazewski theorem and lasalle s invariance principle

the inverse problem for distributive lattices abstract the inverse problem givena in vl n b in vl m andb in vl m find all a in vl n such that a a b b where l is distributive lattice denotes max min composition vl n denotes the set of all vector with n member on l and x a1 a2 an b1 b2 bn ai bj n m is investigated the necessary and sufficient condition for the existence of a solution is shown and an analytical solution is given

travelling wavefronts in the diffusive single species model with allee effect and distributed delay in this paper we consider the diffusive single species model with allee effect and distributed delay time special attention is paid to the existence of travelling wavefront solutions first we shall show that such fronts exist when the convolution kernel assumes the strong generic delay kernel and the delay is sufficiently small then in the non local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times we shall show that such fronts still exist for the weak generic delay kernel and small delay the approach used in this paper is the geometric singular perturbation theory

fuzzy relational equations and the inverse problem abstract the inverse problem concerned with fuzzy relations is investigated the conditions for the existence of a solution are shown and an analytical solution is given a method for the improvement of the solution is proposed

on travelling wavefronts of nicholson s blowflies equation with diffusion this paper is devoted to the study of nicholson s blowflies equation with diffusion a kind of time delayed reaction diffusion for any travelling wavefront with speed c c c is the minimum wave speed we prove that the wavefront is time asymptotically stable when the delay time is sufficiently small and the initial perturbation around the wavefront decays to zero exponentially in space as x but it can be large in other locations the result develops and improves the previous wave stability obtained by mei et al in 2004 the new approach developed in this paper is the comparison principle combined with the technical weighted energy method numerical simulations are also carried out to confirm our theoretical results

convergence under q of p invariant measures on the circle abstract consider the semigroup of maps tn n n where tn x nx mod 1 suppose p and q are multiplicatively independent integers in that they are not both powers of the same integer further suppose that is a borel probability measure invariant ergodic and of positive entropy for tp we show that the sequence of measures tiq converges weak to lebesgue measure on a subsequence of values i of uniform full density

traveling wave solutions in delayed reaction diffusion systems with mixed monotonicity this paper deals with the existence of traveling wave solutions in delayed reaction diffusion systems with mixed monotonicity based on two different mixed quasi monotonicity reaction terms we propose new conditions on the reaction terms and new definitions of upper and lower solutions by using schauder s fixed point theorem and a new cross iteration scheme we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions the general results obtained have been applied to type k monotone and type k competitive diffusive lotka volterra systems

existence of traveling wave solutions for a reaction diffusion equation with distributed delays abstract in this paper we consider a reaction diffusion equation with distributed delays special attention is paid to the existence of traveling wave solutions for special delay kernels using the linear chain trick and the geometric singular perturbation theory we investigate a natural connection between the existence of traveling wave solutions for the reaction diffusion equation with distributed delays and the existence of traveling wave solutions for the corresponding undelayed reaction diffusion equation we show that if the corresponding undelayed reaction diffusion equation has a traveling wave solution then for any sufficiently small delay the delayed reaction diffusion equation also has a traveling wave solution

wave front solutions of a diffusive delay model for populations of daphnia magna abstract in this paper we consider a diffusional food limited population model incorporating a discrete time delay for the case when the delay is small we show that monotone travelling front solutions exist connecting the two uniform steady states of the model the effect of a larger delay is studied numerically suggesting that in this case travelling fronts still exist but lose their monotonicity

a geometric approach in the study of traveling waves for some classes of non monotone reaction diffusion systems abstract in this paper we further extend a recently developed method to investigate the existence of traveling waves solutions and their minimum wave speed for non monotone reaction diffusion systems our approach consists of two steps first we develop a geometrical shooting argument with the aid of the theorem of homotopy invariance on the fundamental group to obtain the positive semi traveling wave solutions for a large class of reaction diffusion systems including the models of predator prey interaction for both predator independent dependent functional responses the models of combustion belousov zhabotinskii reaction si type of disease transmission and the model of biological flow reactor in chemostat next we apply the results obtained from the first step to some models such as the beddinton deangelis model and the model of biolocal flow reactor to show the convergence of these semi traveling wave solutions to an interior equilibrium point by the construction of a lyapunov type function or the convergence of semi traveling waves to another boundary equilibrium point by the further analysis of the asymptotical behavior of semi traveling wave solutions

global stability of wavefronts with minimal speeds for nonlocal dispersal equations with degenerate nonlinearity abstract this paper is concerned with the global stability of wavefronts with minimal speeds for degenerate nonlocal dispersal equations by the method of super and subsolutions and a squeezing technique the wavefront with minimal speed is proved to be globally asymptotically stable with phase shift

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

wavefront solutions of degenerate quasilinear reaction diffusion systems with mixed quasi monotonicity abstract this paper is concerned with the existence of wavefront solutions to a system of degenerate quasilinear reaction diffusion equations of mixed quasi monotone properties in the form u i t d i u i u i f i u x t 0 for i 1 n the important features of this system are that some of the diffusion coefficients d i u i are density dependent and may vanish at certain value of u i and that each function f i is quasi monotone increasing for some components of u u 1 u n and decreasing for other components of u such systems model reaction diffusion processes with density driven diffusion mechanism under certain general conditions we prove the existence of a traveling wave solution that is between a pair of coupled upper and lower solutions a predator prey model with nonlinear diffusion is used as an illustration of application the presence of wavefront solutions flowing toward the coexistence states is established by constructing appropriate upper and lower solutions

sharp oscillatory traveling waves of structured population dynamics model with degenerate diffusion abstract we consider a population dynamics model with degenerate diffusion and time delay we discover sharp oscillatory waves with sharp edges and non decaying oscillations arising from density dependent dispersal and reproduction with age structure degenerate diffusion and bad effect of time delay prevent the use of existing approaches here we develop a new delayed iteration framework to show the existence of these peculiar waves in particular the estimate of the admissible wave speed is highly nontrivial we employ a new phase transform method coupled with the detailed analysis of phase energy furthermore we give a complete characterization of the dynamical behaviors of various kinds of waves our results indicate that simple invasion rules can generate complex wave patterns and provide some interesting insights into the ecological dynamics

travelling waves of the diffusive nicholson s blowflies equation with strong generic delay kernel and non local effect abstract in this paper we consider travelling wave solutions for the diffusive nicholson s blowflies equation incorporating time delay and diffusion special attention is paid to the modelling of the time delay to incorporate associated non local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times for the strong generic delay kernel we show that travelling wave solutions exist provided that the delay is sufficiently small using the geometric singular perturbation theory

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

monotone traveling wavefronts of the kpp fisher delayed equation abstract in the early 2000 s gourley 2000 wu et al 2001 ashwin et al 2002 initiated the study of the positive wavefronts in the delayed kolmogorov petrovskii piskunov fisher equation u t t x u t x u t x 1 u t h x u 0 x r m since then this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction diffusion equations in this paper we give a complete solution to the problem of existence and uniqueness of monotone waves in eq we show that each monotone traveling wave can be found via an iteration procedure the proposed approach is based on the use of special monotone integral operators which are different from the usual wu zou operator and appropriate upper and lower solutions associated to them the analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

stability of traveling wavefronts for a discrete diffusive competition system with three species abstract this paper is concerned with the nonlinear stability of monostable traveling wavefronts for a discrete three species competition diffusion system applying weighted energy method combining with the comparison principle we first show that the traveling wavefronts with large speed are exponentially stable when the initial perturbation around the traveling wave decays exponentially as x but the initial perturbation can be arbitrarily large in other locations then choosing different weight function we improve the stability result to any traveling wavefronts with speed greater than the critical wave speed we have to emphasize that the discrete dispersal operator in the system increases the difficulty of establishing energy estimates

convergence of measures under diagonal actions on homogeneous spaces abstract let be a probability measure on t n 1 where n 2 or 3 suppose is invariant ergodic and has positive entropy with respect to the linear transformation defined by a hyperbolic matrix we get a measure on sl n z sl n r by putting on some unstable horospherical orbit of the right translation of a t diag e t e t e n 1 t t 0 we prove that if the average of with respect to the flow a t has a limit then it must be a scalar multiple of the probability haar measure as an application we show that if the entropy of is large then dirichlet s theorem is not improvable almost surely

stability of steady states and existence of travelling waves in a vector disease model in this paper a host vector model is considered for a disease without immunity in which the current density of infectious vectors is related to the number of infectious hosts at earlier times spatial spread in a region is modelled in the partial integro differential equation by a diffusion term for the general model we first study the stability of the steady states using the contracting convex sets technique when the spatial variable is one dimensional and the delay kernel assumes some special form we establish the existence of travelling wave solutions by using the linear chain trick and the geometric singular perturbation method

spreading speed and wavefronts for parabolic functional differential equations with spatio temporal delays the existence of traveling wavefronts and the spreading speed for a kind of general reaction diffusion system with spatio temporal delays are investigated we obtain the conclusion that there is c 0 being the asymptotic speed of spread and the minimal speed for the system some more delicate analysis techniques have been developed to make the forms of the kernel function g t x and the function f more flexible in our paper a pair of super solution and sub solution have been constructed in order that the existence of traveling wavefronts can be guaranteed there is a biological model as an example in this article which is coincident with this system

determinant theory for fuzzy matrices abstract we study determinant theory for fuzzy square matrices including some boolean matrices and consider the cayley hamilton theorem for these matrices we prove that det a adj a det a det adj a a where adj a denotes the adjoint matrix of a fuzzy matrix a

traveling waves for nonlinear cellular neural networks with distributed delays abstract in this paper we will establish the existence and nonexistence of traveling waves for nonlinear cellular neural networks with finite or infinite distributed delays the dynamics of each given cell depends on itself and its nearest m left or l right neighborhood cells where delays exist in self feedback and left or right neighborhood interactions our approach is to use schauder s fixed point theorem coupled with upper and lower solutions of the integral equation in a suitable banach space further we obtain the exponential asymptotic behavior in the negative infinity and the existence of traveling waves for the minimal wave speed by the limiting argument our results improve and cover some previous works

traveling wavefronts for a time delayed non newtonian filtration equation abstract this paper is concerned with traveling wavefronts for the evolutionary p laplacian with time delay we first establish some necessary and sufficient conditions for the existence of monotone nondecreasing and nonincreasing traveling wavefronts which correspond to definite wave speeds c 1 and c 2 respectively moreover special attention is also paid to the asymptotic behavior of traveling fronts connecting two uniform steady states

generalized traveling waves for time dependent reaction diffusion systems traveling wave solutions in general time dependent including time periodic reaction diffusion equations and systems of equations have attracted great attention in the last two decades the aim of this paper is to study the propagation phenomenon in a general time heterogeneous environment more specifically we investigate generalized traveling wave solutions for a two component time dependent non cooperative reaction diffusion system which has applications in epidemiology and ecology sufficient conditions on the existence and nonexistence of generalized traveling wave solutions are established in the susceptible infectious epidemic model setting generalized traveling waves describe the spatio temporal invasion of a disease into a totally susceptible population in the context of predator prey systems the generalized traveling waves describe the spatial invasion of predators introduced into a new environment where the prey population is at its carrying capacity

travelling waves for a biological reaction diffusion model with spatio temporal delay in this paper we consider the reaction diffusion equations with spatio temporal delay which models the microbial growth in a flow reactor nonlocal spatial term a weighted average in space arises when the individuals have not necessarily been at the same point in space at previous time by employing linear chain technique geometric singular perturbation and the center manifold theorem we prove that the steady travelling wave does not only persist but also it looks qualitatively the same as it do with no delay at all under the introduction of delays at least for small delay

travelling waves for a non monotone bistable equation with delay existence and oscillations we consider a bistable 0 theta 1 being the three constant steady states delayed reaction diffusion equation which serves as a model in population dynamics the problem does not admit any comparison principle this prevents the use of classical technics and as a consequence it is far from obvious to understand the behaviour of a possible travelling wave in infty combining refined it a priori estimates and a leray schauder topological degree argument we construct a travelling wave connecting 0 in infty to lq lq something which is strictly above the unstable equilibrium theta in infty furthemore we present situations additional bound on the nonlinearity or small delay where the wave converges to 1 in infty whereas the wave is shown to oscillate around 1 in infty when typically the delay is large

on the existence of traveling waves for delayed reaction diffusion equations abstract we study the existence of traveling wave solutions for reaction diffusion equations with nonlocal delay where reaction terms are not necessarily monotone the existence of traveling wave solutions for reaction diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the schauder fixed point theorem the smoothness of upper and lower solutions is not required in this paper

stability analysis of heat flow with boundary time varying delay effect abstract in this paper we investigate the stabilization of heat flow with boundary time varying delay effect under some assumptions we prove exponential stability of the solution applying variable norm technique and modified lyapunov functional approach

traveling wave solutions for diffusive predator prey type systems with nonlinear density dependence abstract traveling wave solution for a class of diffusive predator prey system with nonlinear density dependence is considered using methods of topological shooting we show the existence of a non negative traveling wave solution connecting a boundary equilibrium to the co existence steady state with the help of a wazewski like set together with lyapunov function constructed elaborately this means that the traveling wave solution established by huang 2012 can be preserved in the presence of the nonlinear density dependence for the predator and the results of huang 2012 are generalized

on measures invariant under tori on quotients of semisimple groups we classify invariant and ergodic probability measures on arithmetic homogeneous quotients of semisimple s algebraic groups invariant under a maximal split torus in at least one simple local factor and show that the algebraic support of such a measure splits into the product of four homogeneous spaces a torus a homogeneous space on which the measure is up to nite index the haar measure a product of homogeneous spaces on each of which the action degenerates to a rank one action and a homogeneous space in which every element of the action acts with zero entropy

nonlinear stability of traveling wavefronts for competitive cooperative lotka volterra systems of three species abstract this paper is concerned with nonlinear stability of traveling wavefronts for competitive cooperative lotka volterra systems of three species it is proved that all traveling wavefronts with speed c c are exponentially stable in l space by the weighted energy method and comparison principle moreover the time decay rates are obtained by weighted energy estimates

asymptotic patterns of a structured population diffusing in a two dimensional strip abstract in this paper we derive a population model for the growth of a single species on a two dimensional strip with neumann and robin boundary conditions we show that the dynamics of the mature population is governed by a reaction diffusion equation with delayed global interaction using the theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows we obtain the spreading speed c the non existence of traveling waves with wave speed 0 c c and the existence of monotone traveling waves connecting the two equilibria for c c

resolution of the cartesian product of fuzzy sets abstract the problem given a in v n b in v m and b in v m find all a in v n such that a a b b where denotes max min composition x denotes cartesian product and v n denotes the set of all fuzzy vectors with n members is investigated the condition for the existence of a solution is shown and an analytical solution is given

minimal wave speed for a class of non cooperative reaction diffusion systems of three equations abstract in this paper we study the traveling wave solutions and minimal wave speed for a class of non cooperative reaction diffusion systems consisting of three equations based on the eigenvalues a pair of upper lower solutions connecting only the invasion free equilibrium are constructed and the schauder s fixed point theorem is applied to show the existence of traveling semi fronts for an auxiliary system then the existence of traveling semi fronts of original system is obtained by limit arguments the traveling semi fronts are proved to connect another equilibrium if natural birth and death rates are not considered and to be persistent if these rates are incorporated then non existence of bounded traveling semi fronts is obtained by two sided laplace transform then the above results are applied to some disease transmission models and a predator prey model

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

the complete resolution of cartesian products of fuzzy sets abstract a complete solution is given to the cartesian problem given the fuzzy sets a u b v and b v find all fuzzy sets a u such that a a b b where denotes the max min composition this work is an extension of the work by pappis fuzzy sets and systems 26 1988 387 391 and kim et al fuzzy sets and systems 41 1991 293 297

resolution of cartesian products of fuzzy sets abstract the problem given the fuzzy subsets a u b v and b v find all a u such that a a b b where denotes max min composition and x denotes cartesian product is investigated the condition for the existence of a solution is shown and an analytical solution is given

existence and nonexistence of monotone traveling waves for the delayed fisher equation abstract in this paper a new approach based on a shooting method in a half line coupled with the technique of upper lower solution pair is used to study the existence and nonexistence of monotone waves for one form of the delayed fisher equation that does not have the quasimonotonicity property a necessary and sufficient condition is provided this new method can be extended to investigate many other nonlocal and non monotone delayed reaction diffusion equations

delay induced traveling wave fronts in reaction diffusion equations of kpp fisher type this paper explores the impact of delay on the existence of traveling wave fronts in reaction diffusion equations of kpp fisher type for two such equations one being local and the other with nonlocal effect arising from the age structure of the population we show that delay can induce slow traveling wave fronts

travelling wave fronts in reaction diffusion systems with spatio temporal delays this paper deals with the existence of travelling wave fronts in reaction diffusion systems with spatio temporal delays our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system new iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions following this the existence of travelling wave fronts for reaction diffusion systems with spatio temporal delays is established finally we apply the main results to a single species diffusive model with spatio temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

the existence of periodic travelling waves for singularly perturbed predator prey equations via the conley index this paper is concerned with the existence of periodic travelling wave solutions of reactiondiffusion equations which arise as models of predator prey interactions in mathematical ecology the relevant equations are somewhat similar to the fitz hugh nagumo equations and our results apply to this latter system as well in studying the fitz hugh nagumo equations conley 3 i initiated a new topological approach to this problem his method depends on the construction of an isolating neighborhood cf section 2a about a singular periodic solution associated with such a neighborhood is a topological invariant the conley index which when nontrivial implies the existence of a smooth solution near the singular one the new aspects of the present discussion are in the method used to construct the isolating neighborhood in ifi4 and in the computation of the index with regard to the isolating neighborhood our construction is global in that a parameter taken to be small in conley s equations is now allowed to assume large values in order to compute the index we continue our equations to those studied by conley actually we go one step further and continue conley s equations to the van der pol equations crossed with a pair of linear equations admitting a repelling critical point the index for this latter system is easily computed and turns out to be non trivial it follows from the invariance of the index under continuation 21 that the desired

persistence of wavefronts in delayed nonlocal reaction diffusion equations we develop a perturbation argument based on existing results on asymptotic autonomous systems and the fredholm alternative theory that yields the persistence of traveling wavefronts for reaction diffusion equations with nonlocal and delayed nonlinearities when the time lag is relatively small this persistence result holds when the nonlinearity of the corresponding ordinary reaction diffusion system is either monostable or bistable we then illustrate this general result using five different models from population biology epidemiology and bio reactors

spreading speed and traveling waves for a multi type sis epidemic model abstract the theory of asymptotic speeds of spread and monotone traveling waves for monotone semiflows is applied to a multi type sis epidemic model to obtain the spreading speed c and the nonexistence of traveling waves with wave speed c c then the method of upper and lower solutions is used to establish the existence of monotone traveling waves connecting the disease free and endemic equilibria for c c this shows that the spreading speed coincides with the minimum wave speed for monotone traveling waves we also give an affirmative answer to an open problem presented by rass and radcliffe l rass j radcliffe spatial deterministic epidemics math surveys monogr 102 amer math soc providence ri 2003

perron theorem in the monotone iteration method for traveling waves in delayed reaction diffusion equations abstract in this paper we revisit the existence of traveling waves for delayed reaction diffusion equations by the monotone iteration method we show that perron theorem on existence of bounded solution provides a rigorous and constructive framework to find traveling wave solutions of reaction diffusion systems with time delay the method is tried out on two classical examples with delay the predator prey and belousov zhabotinskii models

existence of traveling wave solutions for gause type models of predator prey systems this paper deals with the existence of three types of traveling waves for a general predator prey systems of gause type traveling wave train solution point to point and point to periodic traveling wave solutions applying the methods of wazewski theorem lasalle s invariance principle and hopf bifurcation theorem we obtain the existence results also the minimal wave speed for biological invasion is obtained furthermore some applications are given to illustrate our results

entropy of convolutions on the circle given ergodic p invariant measures f ig on the 1 torus w e give a sharp condition on their entropies guaranteeing that the entropy of the convolution 1 n converges to logp we also prove a variant of this result for joinings of full entropy on in conjunction with a method of host this yields the following denote aeq x qx mod 1 then for every p invariant ergodic with positive entropy 1 n p ni1 n 0 aecn converges weak to lebesgue measure as n i 1 under a certain mild combinatorial condition onfckg for instance the condition is satisfled if p 10 and ck 2 k 6 k or ck 2 2 k this extends a result of johnson and rudolph who considered the sequence ck q k when p and q are multiplicatively independent we also obtain the following corollary concerning hausdorfi dimension of sum sets for any sequence fsig of p invariant closed subsets of i f p dimh si j log dimh si j 1 then dimh s1 sn i 1

travelling waves for delayed reaction diffusion equations with global response we develop a new approach to obtain the existence of travelling wave solutions for reaction diffusion equations with delayed non local response the approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain banach space coupled with an index formula of the associated fredholm operator and some careful estimation of the nonlinear perturbation the general result relates the existence of travelling wave solutions to the existence of heteroclinic connecting orbits of a corresponding functional differential equation and this result is illustrated by an application to a model describing the population growth when the species has two age classes and the diffusion of the individual during the maturation process leads to an interesting non local and delayed response for the matured population

stability of traveling waves in a population dynamics model with spatio temporal delay abstract in this paper we are concerned with the stability of all traveling waves for a population dynamics model with spatio temporal delay by the weighted energy method combining comparison principle the global exponential stability of all traveling waves for the model is established even including the slower waves whose wave speed is close to the critical speed

statistical mechanics of surjective cellular automata reversible cellular automata are seen as microscopic physical models and their states of macroscopic equilibrium are described using invariant probability measures we establish a connection between the invariance of gibbs measures and the conservation of additive quantities in surjective cellular automata namely we show that the simplex of shift invariant gibbs measures associated to a hamiltonian is invariant under a surjective cellular automaton if and only if the cellular automaton conserves the hamiltonian a special case is the well known invariance of the uniform bernoulli measure under surjective cellular automata which corresponds to the conservation of the trivial hamiltonian as an application we obtain results indicating the lack of non trivial gibbs or markov invariant measures for sufficiently chaotic cellular automata we discuss the relevance of the randomization property of algebraic cellular automata to the problem of approach to macroscopic equilibrium and pose several open questions as an aside a shift invariant pre image of a gibbs measure under a pre injective factor map between shifts of finite type turns out to be always a gibbs measure we provide a sufficient condition under which the image of a gibbs measure under a pre injective factor map is not a gibbs measure we point out a potential application of pre injective factor maps as a tool in the study of phase transitions in statistical mechanical models

traveling wavefronts for time delayed reaction diffusion equation ii nonlocal nonlinearity abstract in this paper we study a class of time delayed reaction diffusion equation with local nonlinearity for the birth rate for all wavefronts with the speed c c where c 0 is the critical wave speed we prove that these wavefronts are asymptotically stable when the initial perturbation around the traveling waves decays exponentially as x but the initial perturbation can be arbitrarily large in other locations this essentially improves the stability results obtained by mei so li and shen m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 for the speed c 2 d m e p d m with small initial perturbation and by lin and mei c k lin m mei on travelling wavefronts of the nicholson s blowflies equations with diffusion submitted for publication for c c with sufficiently small delay time r 0 the approach adopted in this paper is the technical weighted energy method used in m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 but inspired by gourley s a gourley linear stability of travelling fronts in an age structured reaction diffusion population model quart j mech appl math 58 2005 257 268 and based on the property of the critical wavefronts the weight function is carefully selected and it plays a key role in proving the stability for any c c and for an arbitrary time delay r 0

traveling wave solutions in a delayed diffusive competition system abstract in this paper we first investigate the existence of traveling wave fronts in a delayed diffusive competition system by constructing a pair of upper and lower solutions then we consider the asymptotic behavior of traveling wave solutions at the minus plus infinity by means of the bilateral laplace transform finally the monotonicity and uniqueness up to the translation of traveling wave solutions are also obtained by the strong comparison principle and the sliding method

pyramidal traveling fronts in a nonlocal delayed diffusion equation abstract recently there have been great progresses on the study of nonplanar traveling wave solutions of reaction diffusion equations in this paper we study the pyramidal traveling fronts of nonlocal delayed diffusion equation in r n with n 2 by using the comparison principle and establishing super and subsolution since the effect of nonlocal delay we show that nonlocal delayed diffusion equation in n dimensional space has a pyramidal traveling front u t x v x x n s t toward x n axis for each s c 0 in particular two dimensional traveling curved front and three dimensional pyramidal fronts for nonlocal delayed diffusion equation in r 2 and r 3 are also established respectively moreover we also extend our results to generally nonlocal delayed reaction diffusion equation

traveling waves for a time delayed newtonian filtration equation abstract this paper deals with traveling wave solutions for a degenerate parabolic equation with time delay we first establish the necessary and sufficient conditions to the existence of monotone nonincreasing and nondecreasing traveling wave solutions which correspond to a unique wave speed c respectively it will be shown that the traveling wave may be a semi finite or infinite traveling wave under different exponents furthermore we give an accurate estimation on the convergent rate for the semi finite or infinite traveling waves

spreading speeds and traveling wavefronts for second order integrodifference equations this paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations by introducing an auxiliary integrodifference system the spreading speed is established for the integrodifference equation it is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts furthermore we prove that the traveling wavefronts are stable by applying the squeezing technique finally we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology

asymptotic stability of traveling wave fronts in nonlocal reaction diffusion equations with delay abstract this paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction diffusion equations with delay under monostable assumption we prove that the traveling wave front is exponentially stable by means of the technical weighted energy method when the initial perturbation around the wave is suitable small in a weighted norm the exponential convergent rate is also obtained finally we apply our results to some population models and obtain some new results which recover complement and or improve a number of existing ones

existence of travelling wave solutions of predator prey systems via the connection index we consider a reaction diffusion system which arises as a model of predator prey interactions in mathematical ecology the system admits four constant equilibria two of which are stable the main result is an existence theorem for travelling wave solutions which connect the two stable equilibria most previous efforts with regard to travelling waves for systems employ singular perturbations to locate the connecting orbit the new aspect of the present discussion lies in devising some novel methods for locating the connecting solution in phase space which do not require that the equations be singularly perturbed in certain cases the main result holds for an arbitrary choice of diffusion coefficients

general conditions for the existence of a critical point periodic wave front connection for reaction diffusion systems on etudie l existence de fronts d onde plane heteroclines pour les equations u t d u f u et l equation des etats homogenes du dt f u u r n r r m x t u x t u i x t 1 i m d est une matrice symetrique definie positive

reduction to a single closed equation for 2 by 2 reaction diffusion systems of lotka volterra type we consider general models of coupled reaction diffusion systems for interacting variants of a species when the total population becomes large with intensive competition we prove that the frequency i e proportion of a variant can be approached by the solution of a single reaction diffusion equation through a singular limit method and a relative compactness argument applying this result we retrieve the classical bistable equation for wolbachia s spread into an arthropod population from a system modeling interaction between infected and uninfected individuals

a phase plane discussion of convergence to travelling fronts for nonlinear diffusion the paper is concerned with the asymptotic behavior as t of solutions u x t of the equation u t u xx f left u right 0 x in left infty infty right in the case f 0 f 1 0 with f u non positive for u 0 sufficiently close to zero and f u non negative for u 1 sufficiently close to 1 this guarantees the uniqueness but not the existence of a travelling front solution u u x ct u 0 u and it is shown in essence that solutions with monotonic initial data converge to a translate of this travelling front if it exists and to a stacked combination of travelling fronts if it does not the approach is to use the monotonicity to take u and t as independent variables and p ux as the dependent variable and to apply ideas of sub and super solutions to the diffusion equation for p

existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay this paper is concerned with the existence uniqueness and globally asymptotic stability of traveling wave fronts in the quasi monotone reaction advection diffusion equations with nonlocal delay under bistable assumption we construct various pairs of super and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front up to translation which is monotonically increasing and globally asymptotically stable with phase shift the influence of advection on the propagation speed is also considered comparing with the previous results our results recovers and or improves a number of existing ones in particular these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay some new results are obtained

periodic traveling waves in a reaction diffusion model with chemotaxis and nonlocal delay effect abstract in this paper we study the existence of periodic traveling wave solutions with large wave speed for a reaction diffusion model with chemotaxis and nonlocal delay effect by applying the perturbation method the proof relies on an abstract formulation of the wave profile as a solution of an operator equation in a certain banach space coupled with the lyapunov schmidt reduction and the implicit function theorem

entire solutions in monostable reaction diffusion equations with delayed nonlinearity abstract entire solutions for monostable reaction diffusion equations with nonlocal delay in one dimensional spatial domain are considered a comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory key techniques include the characterization of the asymptotic behaviors of solutions as t in term of appropriate subsolutions and supersolutions two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

bistable wavefronts in a diffusive and competitive lotka volterra type system with nonlocal delays abstract a diffusive lotka volterra type model with nonlocal delays for two competitive species is considered the existence of a traveling wavefront analogous to a bistable wavefront for a single species is proved by transforming the system with nonlocal delays to a four dimensional system without delay furthermore in order to prove the asymptotic stability up to translation of bistable wavefronts of the system the existence regularity and comparison theorem of solutions of the corresponding cauchy problem are first established for the systems on r by appealing to the theory of abstract functional differential equations the asymptotic stability up to translation of bistable wavefronts are then proved by spectral methods in particular we also prove that the spreading speed is unique by upper and lower solutions technique from the point of view of ecology our results indicate that the nonlocal delays appeared in the interaction terms are not sensitive to the invasion of species of spatial isolation

fuzzy rational choice functions we introduce a concept of fuzzy rationality of a choice function characterize fuzzy rational choice functions and study the semigroup of all fuzzy rational choice functions on a finite set

traveling wave solutions in n dimensional delayed reaction diffusion systems with mixed monotonicity this paper deals with the existence of traveling wave solutions for n components delayed reaction diffusion systems with mixed monotonicity based on a certain kind of mixed quasimonotonicity reaction terms of higher dimension we propose new conditions on the reaction terms and new definitions of upper and lower solutions by using schauder s fixed point theorem and a cross iteration scheme we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions the general results obtained will be applied to type k monotone diffusive lotka volterra systems of higher dimension

positive heteroclinics and traveling waves for scalar population models with a single delay the existence of positive heteroclinic solutions is proven for a class of scalar population models with one discrete delay traveling wave solutions for scalar delayed reaction diusion equations are also obtained as perturbations of heteroclinic solutions of the associated equation without diusion as an illustration the results are applied to the nicholson s blowflies equation with diusion n t t x d 2n x2 t x n t x pn t x e an t x in the case of p e for which the nonlinearity is non monotone

traveling waves for time delayed reaction diffusion equations with degenerate diffusion abstract this paper is concerned with time delayed reaction diffusion equations with degenerate diffusion when the term for birth rate is a nonlocal integral with a heat kernel the family of minimum wave speeds corresponding to all the degenerate diffusion coefficients is proved to admit a uniform positive infimum however when the term for birth rate is local there is no positive infimum of all the minimum wave speeds this difference indicates that the nonlocal effect plays a role as laplacian such that a positive lower bound independent of the degenerate diffusion exists for the minimum wave speeds the approach adopted for the proof is the monotone technique with the viscosity vanishing method the degeneracy of diffusion for the equation causes us essential difficulty in the proof a number of numerical simulations are also carried out at the end of the paper which further numerically confirm our theoretical results