global boundedness for a delay differential equation on etudie l inequation t u u t x u t x 1 u t x on montre que les solutions non negatives du probleme de dirichlet dans un intervalle borne restent bornees lorsque le temps croit indefiniment dans un domaine de plus grande dimension cette propriete n a lieu que si le retard n est pas trop grand

on the spaces lp x ω and wm p x ω in this paper we present some basic results on the generalized lebesgue spaces l p x omega and generalized lebesgue sobolev spaces w m w p x omega these results provide the necessary framework for the study of variational problems and elliptic equations with non standard p x growth conditions c 2001 academic press

hopf transcritical bifurcation in toxic phytoplankton zooplankton model with delay abstract in this paper a phytoplankton zooplankton model with toxic liberation delay is considered firstly the critical values of hopf bifurcation transcritical bifurcation and hopf transcritical bifurcation are given and to give more detailed information about the periodic oscillations the direction and stability of hopf bifurcation is studied by using the normal form theory and center manifold theorem then we give the detailed bifurcation set by calculating the universal unfoldings near the hopf transcritical bifurcation point finally we show that the plankton system may exhibit quasi periodic oscillations which are verified both theoretically and numerically and explain the experimental observed fluctuation phenomenon of plankton population

composition algebras with large derivation algebras abstract the finite dimensional flexible composition algebras include the hurwitz algebras composition algebras with unit element but also other interesting classes of algebras the para hurwitz and the okubo algebras the above mentioned algebras present many symmetries and this is reflected in their large derivation algebras in the present paper we study the opposite question what can be said about the composition algebras if we have some information about their derivation algebras our main result is the classification of all the composition algebras with such large derivation algebras

a note on hopf bifurcations in a delayed diffusive lotka volterra predator prey system the diffusive lotka volterra predator prey system with two delays is reconsidered here the stability of the coexistence equilibrium and associated hopf bifurcation are investigated by analyzing the characteristic equations and our results complement earlier ones we also obtain that in a special case a hopf bifurcation of spatial inhomogeneous periodic solutions occurs in the system

permanence and extinction in nonlinear single and multiple species system with diffusion in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments average conditions are obtained for the permanence and extinction of the systems considered the results obtained in this paper generalize the main results of cui and chen the effect of diffusion on the time varying logistic population growth comput math appl 36 3 1998 1 9 permanence and extinction in logistic and lotka volterra systems with diffusion j math anal appl 258 2 2001 512 535

periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model a neutral multispecies logarithmic population model is proposed in this paper by using the contraction mapping principle and constructing a suitable lyapunov functional a set of easily applicable criteria are established for the existence uniqueness and global attractivity of positive periodic solution positive almost periodic solution of the model

espaces de lipschitz et inegalites de poincare resume in the setting of infinite graphs and non compact riemannian manifolds we show that suitable families of poincare inequalities yield global embeddings of sobolev spaces into lipschitz spaces as well as trudinger type inequalities this applies for example to cocompact coverings and to manifolds that are roughly isometric to a manifold with nonnegative ricci curvature in the process we give several reformulations of the sobolev inequalities and in particular show their equivalence with some l p faber krahn inequalities we also give an interpretation of some of our results in terms of distances on graphs associated with the l p norm of the gradient

hopf bifurcation in a delayed reaction diffusion advection population model abstract in this paper we investigate a reaction diffusion advection model with time delay effect the stability instability of the spatially nonhomogeneous positive steady state and the associated hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction diffusion advection model and the model can exhibit oscillatory pattern through hopf bifurcation the effect of advection on hopf bifurcation values is also considered and our results suggest that hopf bifurcation is more likely to occur when the advection rate increases

dynamics analysis of a delayed diffusive predator prey system with non smooth continuous threshold harvesting this paper deals with a delayed reaction diffusion predator prey model with non smooth harvesting sufficient conditions for the local stability of the interior equilibrium and the existence of discontinuous hopf bifurcations and classical hopf bifurcations are obtained by using the theory of partial functional differential equations finally numerical simulation results are presented to validate the theoretical analysis

hopf bifurcation in a diffusive lotka volterra type system with nonlocal delay effect abstract the dynamics of a diffusive lotka volterra type model for two species with nonlocal delay effect and dirichlet boundary conditions is investigated in this paper the existence and multiplicity of spatially nonhomogeneous steady state solutions are obtained by means of lyapunov schmidt reduction the stability of spatially nonhomogeneous steady state solutions and the existence of hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system by the normal form theory and the center manifold reduction the stability and bifurcation direction of hopf bifurcating periodic orbits are derived finally our theoretical results are illustrated by a model with homogeneous kernels and one dimensional spatial domain

dynamics in a diffusive predator prey system with ratio dependent predator influence abstract a diffusive predator prey system with predator functional response subject to neumann boundary conditions is considered existence nonexistence and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation hopf and steady state bifurcation analyses are carried out in detail these results provide theoretical evidences to the complex spatio temporal dynamics found by numerical simulation

permanence and global attractivity of a delayed periodic logistic equation in this paper we consider the delayed periodic logistic equation n t n t a t b t np t t c t nq t t which describes the evolution of a single species sufficient conditions which guarantee the permanence and the globally attractivity of the system are obtained

sobolev embeddings in metric measure spaces with variable dimension in this article we study metric measure spaces with variable dimension we consider lebesgue spaces on these sets and embeddings of the riesz potential in these spaces we also investigate hajlasz type sobolev spaces and prove sobolev and trudinger inequalities with optimal exponents all of these questions lead naturally to function spaces with variable exponents

on the periodic solutions of periodic multi species kolmogorov type competitive system with delays and feedback controls abstract in this paper we consider a periodic multi species kolmogorov type competitive system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive periodic solution of the system are obtained as application the existence of the positive periodic solution of a kind of nonlinear competitive model with delays and feedback controls is discussed

spatially nonhomogeneous equilibrium in a reaction diffusion system with distributed delay we consider a reaction diffusion system with general time delayed growth rate and kernel functions the existence and stability of the positive spatially nonhomogeneous steady state solution are obtained moreover taking minimal time delay as the bifurcation parameter hopf bifurcation near the steady state solution is proved to occur at a critical value 0 especially the hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold the general results are applied to competitive and cooperative systems with weak or strong kernel function respectively

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

sobolev spaces with variable exponents on complete manifolds we study variable exponent function spaces on complete non compact riemannian manifolds using classic assumptions on the geometry continuous embeddings between sobolev and holder function spaces are obtained we prove compact embeddings of h invariant sobolev spaces where h is a compact lie subgroup of the group of isometries of the manifold as an application we prove the existence of non trivial solutions to non homogeneous q x laplace equations

sobolev spaces with variable exponents on riemannian manifolds abstract in this article we study variable exponent sobolev spaces on riemannian manifolds the spaces are examined in the case of compact manifolds continuous and compact embeddings are discussed the paper contains an example of the application of the theory to elliptic equations on compact manifolds

invariant affine connections on lie groups the space of bi invariant affine connections is determined for arbitrary compact lie groups in particular there is a surprising new family of such connections on su n

global asymptotic stability in n species non autonomous lotka volterra competitive systems with infinite delays and feedback control abstract a non autonomous lotka volterra competition system with infinite delays and feedback control and without dominating instantaneous negative feedback is investigated by means of a suitable lyapunov functional sufficient conditions are derived for the global asymptotic stability of the system some new results are obtained

dirichlet problem for the diffusive nicholson s blowflies equation abstract the object of this paper is to consider the asymptotic behavior of solutions of the diffusive nicholson s blowflies equation under dirichlet boundary condition a new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay when monotone or quasi monotone conditions fail to apply this approach should be applicable to other dirichlet problems as well even though our analysis is tailored to the diffusive nicholson s blowflies equation

hopf bifurcation and global stability of a delayed predator prey model with prey harvesting in this paper we consider a delayed prey predator model with modified leslie gower term and michaelis menten type prey harvesting regarding time delay as a bifurcation parameter and using the normal form and center manifold theorem of functional differential equations and partial differential equations we obtain the existence stability and direction of periodic solutions of functional differential equations and partial differential equations respectively numerical simulations are carried out to depict our theoretical analysis

volumes of small balls on open manifolds lower bounds and examples question under what curvature assumptions on a complete open manifold is the volume of balls of a fixed radius bounded below independent of the center point xx two theorems establish such assumptions and two examples sharply limit their weakening in particular we give an example of a metric on r4 extending to higher dimensions of positive ricci curvature whose sectional curvatures decay to 0 and such that the volume of balls goes uniformly to 0 as the center goes to infinity 0 introduction the following question came up in discussions of the first author with peter li under what curvature assumptions on a complete open manifold m can one find a constant c m r such that the volume of balls b x r can be bounded from below independent of the midpoint x 0 1 vol b x r c m r note that in the presence of a lower bound on the ricci curvature one needs to prove the above inequality only for some r since the bishop gromov volume comparison theorem gr p 124 then gives a bound c m r for r c n rn in dimension 2 theorem a below is a satisfyingpositive answer since the assumptions do not imply a lower bound on the injectivity radius while any weakening of the assumptions leads to immediate counterexamples theorem a if m2 is complete with curvature k o then there exist c m such that for radii r c m r2 in higher dimensions however we have example 1 there are convex hypersurfaces md in rd 1 such that for d 3 no lower bounds as in 0 1 exist for md in dimensions 2 we therefore assume an upper curvature bound but then one gets uniform control even on the injectivity radius the following theorem has been rediscovered several times received by the editors august 10 1987 1980 mathematics subject classification 1985 revision primary 53c20 secondary 53a07 research supported by nsf grant mcs 7g01780 and the sloan foundation both authors were supported by invitations to the i h e s and the m s r i r 1988 american mathematical society 0002 9947 88 1 00 25 per page

asymptotic periodicity of a food limited diffusive population model with time delay abstract in this paper a general reaction diffusion food limited population model with time delay is proposed accordingly the existence and uniqueness of the periodic solutions for the boundary value problem and the asymptotic periodicity of the initial boundary value problem are considered finally the effect of the time delay on the asymptotic behavior of the solutions is given

the effects of temporal delays in a model for a food limited diffusing population we consider an adaptation of the well known logistic equation in mathematical ecology in which the population is assumed to diffuse and for which the average growth rate is a function of some specified delayed argument using a combination of analytical and numerical techniques we investigate the existence uniqueness and asymptotic stability of the nonnegative steady states of this equation

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

periodicity in a food limited population model with toxicants and state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a food limited population model with toxicant and state dependent delays that is du t dt u t r t a t u t j 1 m b j t u t j t u t k t c t u t j 1 m d j t u t j t u t where r t k t a t bj t dj t j 1 2 m are continuous real valued periodic functions with period 0 and r t k t a t 0 bj t dj t 0 j 1 2 m are periodic continuous functions with period 0 j j are periodic with respect to their first arguments some new results are obtained

on some algebras related to simple lie triple systems abstract the set hom der t t f t t is determined for any simple finite dimensional lie triple system t over a field f of characteristic zero it turns out that it contains nontrivial elements if and only if t is related to a simple jordan algebra in particular this provides a new proof of the determination by laquer of the invariant affine connections in the simply connected compact irreducible riemannian symmetric spaces

global attractivity and oscillations in a periodic delay logistic equation abstract sufficient conditions are obtained for the global attractivity of a positive periodic solution of the delay logistic equation dx t dt r t x t 1 x t n k t where r and k are positive periodic functions of period and n is a positive integer sufficient conditions are also obtained for all solutions to be oscillatory about k

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

permanence of a delayed non autonomous gilpin ayala competition model abstract in this paper we consider a delayed non autonomous n species gilpin ayala competitive system which is more general and more realistic then classical lotka volterra competition model by means of ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions for the permanence of the system it is shown that our result is the generalization of those of zhao et al j d zhao j f jiang a c lazer the permanence and global attractivity in a nonautonomous lotka volterra system nonlinear analysis real world applications 5 4 2004 265 276 our results also supplement the results of fan and wang m fan k wang global periodic solutions of a generalized n species gilpin ayala competition model computer and mathematics with applications 40 2000 1141 1151

hopf bifurcation in a reaction diffusion equation with distributed delay and dirichlet boundary condition abstract the stability and hopf bifurcation of the positive steady state to a general scalar reaction diffusion equation with distributed delay and dirichlet boundary condition are investigated in this paper the time delay follows a gamma distribution function through analyzing the corresponding eigenvalue problems we rigorously show that hopf bifurcations will occur when the shape parameter n 1 and the steady state is always stable when n 0 by computing normal form on the center manifold the direction of hopf bifurcation and the stability of the periodic orbits can also be determined under a general setting our results show that the number of critical values of delay for hopf bifurcation is finite and increasing in n which is significantly different from the discrete delay case and the first hopf bifurcation value is decreasing in n examples from population biology and numerical simulations are used to illustrate the theoretical results

stability hopf bifurcations and spatial patterns in a delayed diffusive predator prey model with herd behavior in this paper we consider a delayed diffusive predator prey model with herd behavior firstly by choosing the appropriate bifurcation parameter the stability of the positive equilibria and the existence of hopf bifurcations induced by diffusion and delay respectively are investigated by analyzing the corresponding characteristic equation then applying the normal form theory and the center manifold argument for partial functional differential equations the formula determining the properties of the hopf bifurcation are obtained furthermore the instability of the hopf bifurcation leads to the emergence of spatial patterns finally some numerical simulations are also carried out to illustrate and expand the theoretical results

symmetry and compact embeddings for critical exponents in metric measure spaces abstract we obtain a compact sobolev embedding for h invariant functions in compact metric measure spaces where h is a subgroup of the measure preserving bijections in riemannian manifolds h is a subgroup of the volume preserving diffeomorphisms a compact embedding for the critical exponents follows the results can be viewed as an extension of sobolev embeddings of functions invariant under isometries in compact manifolds

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

spatiotemporal dynamics induced by delay and diffusion in a predator prey model with mutual interference among the predator abstract in this work we study a reaction diffusion predator prey model with mutual interference among the predators while searching for food we prove that the model exhibits bistability which indicates that there are no patterns for our model when time delay is incorporated into the model multiple stability switches phenomenon of positive constant steady state emerged by taking delay as a bifurcation parameter the hopf bifurcations at the positive constant steady state are proved to occur for a sequence of critical values of the delay the algorithm for determining the direction and the stability of the bifurcating periodic solutions is also derived the delay diffusion driven turing instability of the positive constant steady state is investigated our results show that delay and diffusion can create periodic oscillatory patterns of spatially homogeneous and inhomogeneous and turing patterns

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

stability and bifurcation analysis of a reaction diffusion equation with spatio temporal delay abstract the spatio temporal patterns of a general reaction diffusion equation with non local delay are considered by analyzing the characteristic equations and applying the complex plane theory the stability of the constant steady state and the possible hopf bifurcations are obtained with the mean delay as a bifurcation parameter the absolute stable conditional stable and unstable region can be explicitly divided by the coefficients of the term without delay and the term with non local delay by investigating the effect of any weight function on the dynamics of the system we establish the existence of spatially homogeneous and inhomogeneous bifurcating periodic solutions and the algorithm for determining the direction and stability of hopf bifurcation is derived by computing the normal form on the center manifold the result shows that for the case of strong kernel the average delay may induce the stability switches finally the theoretical results are applied to a diffusive food limited population model numerical simulations show the existence of the orbit connecting the unstable spatially inhomogeneous periodic solutions to stable spatially homogeneous periodic solutions

on a periodic multi species ecological model a periodic predator prey model with m predators and n preys is proposed in this paper which can be seen as the modification of the traditional lotka volterra model by using comparison theorem the ultimately bounded region of the system is obtained by using comparison theorem and brouwer fixed point theorem sufficient conditions with guarantee the existence of a positive periodic solution of the system is obtained finally by constructing a suitable lyapunov function some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of system the results obtained here generalized the main results of j d zhao w c chen global asymptotic stability of a periodic ecological model applied mathematics and computation 147 3 2004 881 892

dynamics of a diffusion reaction prey predator model with delay in prey effects of delay and spatial components abstract we study the complex dynamics of a monod haldane type predator prey interaction model that incorporates 1 a constant time delay in the prey growth and 2 diffusion in both prey and predator we provide the rigorous results of our system including the asymptotic stability of a positive equilibrium hopf bifurcation and the direction of hopf bifurcation and the stability of bifurcated periodic solutions we also perform numerical simulations on the effects of diffusion or and delay when the corresponding ode model has either a unique interior equilibrium with two interior attractors or two interior equilibria our theoretical and numerical results show that diffusion can either stabilize or destabilize the system large delay could destabilize the system and the combination of diffusion and delay could intensify the instability of the system moreover when the corresponding ode system has two interior equilibria diffusion or time delay in prey or both could lead to the extinction of predator our results may provide us useful biological insights on population managements for prey predator interaction systems

global attractivity in a food limited population model with impulsive effects abstract sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay logistic equation with impulsive effect n t r t n t k n p t k c t n p t n k n k exp i k ln n k k p where r t c t are continuous functions p k are positive constants and k k 1 denotes the sequence of impulsive time which assumed to be strictly increasing some special cases are also considered

formulation of the normal form of turing hopf bifurcation in partial functional differential equations abstract turing hopf bifurcation is considered as an important mechanism for generating complex spatio temporal patterns in dynamical systems in this work the normal form up to the third order for the hopf steady state bifurcation which includes the turing hopf bifurcation of a general system of partial functional differential equations pfdes in a bounded spatial region of any dimension is derived based on the center manifold and the normal form theories of pfdes the explicit formula for the coefficients in the normal form of hopf steady state bifurcation are presented concisely in a matrix form which makes it more convenient in not only symbolic derivation but also numerical implementation this provides an approach of showing the existence and stability of stationary and time periodic solutions with spatial heterogeneity the derived formulas are also applicable to partial differential equations and functional differential equations

on diffusive population models with toxicants and time delays in this article we study the global stability in reaction diffusion models for single species population growth under environmental toxicants with or without time delays the existence and uniqueness of a positive steady state solution are established in those models it is shown that as long as the magnitude of the instantaneous self limitation and toxicant effects is larger than that of the time delay effects in the model with delays the solution of both reaction diffusion systems has the same asymptotic behavior extinction or converging to the positive steady state solution depending on the growth rate of the species numerical simulations for both cases with or without time delays are demonstrated for the purpose of comparison

dynamical analysis of a logistic equation with spatio temporal delay this paper is concerned with a logistic equation with spatio temporal delay the local asymptotic behavior of positive constant steady state solution of the equation is considered in particular by using the iterative technique sufficient conditions are established for the existence of traveling wave front solution connecting the zero and the positive constant steady state solution finally numerical simulations supporting the theoretical analysis are also included

on lie admissible algebras whose commutator lie algebras are lie subalgebras of prime associative algebras abstract we describe third power associative multiplications on noncentral lie ideals of prime algebras and skew elements of prime algebras with involution provided that x y y x x y for all x y and the prime algebras in question do not satisfy polynomial identities of low degree we also obtain necessary and sufficient conditions for these multiplications to be fourth power associative or flexible

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

environmental periodicity and time delays in a food limited population model abstract sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the food limited population system modelled by the equation n t r t k t n t m k t c t r t n t m where m is a nonnegative integer and k r c are continuous positive periodic functions of period

variable exponent functionals in image restoration abstract we study a functional with variable exponent 1 p x 2 which provides a model for image denoising and restoration here p x is defined by the gradient information in the observed image the diffusion derived from the proposed model is between total variation based regularization and gaussian smoothing the diffusion speed of the corresponding heat equation is tuned by the variable exponent p x the minimization problem and its associated flow in a weakened formulation are discussed the existence uniqueness stability and long time behavior of the proposed model are established in the variable exponent functional space w 1 p x experimental results illustrate the effectiveness of the model in image restoration

cordes nirenberg theory in variable exponent spaces abstract we study regularity of weak solutions to uniformly elliptic equations in the variable holder spaces assuming continuity of the coefficients of the operator the holder continuity of the solution is proved moreover assuming holder continuity of the coefficients we prove that the weak gradient is holder continuous

nonautonomous lotka volterra systems with delays abstract the paper studies the general nonautonomous lotka volterra multispecies systems with finite delays the ultimate boundedness permanence global attractivity and existence and uniqueness of strictly positive solutions positive periodic solutions and almost periodic solutions are obtained these results are basically an extension of the known results for nonautonomous lotka volterra multispecies systems without delay to systems with delay

dynamics of the diffusive nicholson s blowflies equation with distributed delay in this paper we study the diffusive nicholson s blowflies equation generalizing previous works we model the generation delay by using an integral convolution over all past times and results are obtained for general delay kernels as far as possible the linearized stability of the non zero uniform steady state is studied in detail mainly by using the principle of the argument global stability both of this state and of the zero state are studied by using energy methods and by employing a comparison principle for delay equations finally we consider what bifurcations are possible from the non zero uniform state in the case when it is unstable

stability and bifurcation in a reaction diffusion model with nonlocal delay effect in this paper the existence stability and multiplicity of spatially nonhomogeneous steady state solution and periodic solutions for a reaction diffusion model with nonlocal delay effect and dirichlet boundary condition are investigated by using lyapunov schmidt reduction moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

global attractivity in an almost periodic multi species nonlinear ecological model abstract a nonlinear almost periodic predator prey model with n preys and m predators is studied in this paper which can be seen as the modification of the traditional multi species lotka volterra predator prey model for general nonautonomous case by using the differential inequality theory we obtain the sufficient conditions which guarantee the uniform persistence and nonpersistence of the system after that by constructing a suitable lyapunov function some sufficient conditions are obtained which ensure the global attractivity of the system for almost periodic case by constructing a suitable lyapunov function sufficient conditions which guarantee the existence of an unique globally attractive positive almost periodic solution of the system are obtained examples together with their numeric simulations show the feasibility of our main results

hopf bifurcation for a delayed predator prey diffusion system with dirichlet boundary condition a delayed predator prey diffusion system with beddington deangelis functional response under dirichlet boundary condition is investigated the existence and stability of the positive spatially nonhomogeneous steady state solution are obtained via the implicit function theorem moreover taking feedback time delay as the bifurcation parameter hopf bifurcation near the positive steady state solution is proved to occur at a sequence of critical values we can show that feedback time delay can induce nonhomogeneous periodic oscillatory patterns the direction of hopf bifurcation is forward when parameter m in model 1 2 is sufficiently large numerical simulations and numerical solutions are presented to illustrate our theoretical results

on evolutionary volterra equations with state dependent delay abstract in this work we study topological properties of the solution set of abstract volterra equations with state dependent delay particularly we ensure that such a set is a nonempty compact and connected set as application we consider our abstract results in the framework of integro differential equations coming from viscoelasticity theory

on the uniform stability for a food limited population model with time delay in this paper we provide sufficient conditions which guarantee the uniform stability as well as asymptotic stability of the positive equilibrium for a food limited population model with time delay

global attractivity of the diffusive nicholson blowflies equation with neumann boundary condition a non monotone case abstract in this paper we establish the global attractivity of the positive steady state of the diffusive nicholson s equation with homogeneous neumann boundary value under a condition that makes the equation a non monotone dynamical system to achieve this we develop a novel method combining a dynamical systems argument with maximum principle and some subtle inequalities

stability and hopf bifurcation in a diffusive logistic population model with nonlocal delay effect abstract a reaction diffusion model with logistic type growth nonlocal delay effect and dirichlet boundary condition is considered and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior the stability of the positive spatially nonhomogeneous positive equilibrium and associated hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel

compact imbedding theorems with symmetry of strauss lions type for the space w1 p x ω abstract in this paper we extend some compact imbedding theorems of strauss lions type to the space w 1 p x when the domain has some symmetric properties and p x satisfies some conditions

dynamic behaviors of a delay differential equation model of plankton allelopathy in this paper we consider a modified delay differential equation model of the growth of n species of plankton having competitive and allelopathic effects on each other we first obtain the sufficient conditions which guarantee the permanence of the system as a corollary for periodic case we obtain a set of delay dependent condition which ensures the existence of at least one positive periodic solution of the system after that by means of a suitable lyapunov functional sufficient conditions are derived for the global attractivity of the system for the two dimensional case under some suitable assumptions we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation examples show the feasibility of the main results

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

pattern formation of an epidemic model with time delay abstract one of the central issues in epidemiology is the study of the distribution of disease and time delay widely exists in the process of disease spread thus in this paper we presented an epidemic model with spatial diffusion and time delay by mathematical analysis we find two different types of instability one is the diffusion induced instability and the other one is delay induced instability moreover we derive the corresponding patterns by performing a series of numerical simulations the obtained results show that the interaction of diffusion and time delay may give rise to rich dynamics in epidemic systems

stability and bifurcations in a nonlocal delayed reaction diffusion population model abstract a nonlocal delayed reaction diffusion equation with dirichlet boundary condition is considered in this paper it is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium the stability instability of the bifurcated positive equilibrium and associated hopf bifurcation are investigated providing us with a complete picture of the dynamics

stability analysis of a stage structure model with spatiotemporal delay effect this paper is concerned with a stage structure model with spatiotemporal delay and homogeneous dirichlet boundary condition the existence of steady state solution bifurcating from the trivial equilibrium is obtained by using lyapunovschmidt reduction the stability analysis of the positive spatially nonhomogeneous steady state solution is investigated by a detailed analysis of the characteristic equation using the properties of the omega limit set we obtain the global convergence of the solution with finite delay

color algebras and affine connections on s6 the classification of algebras having a given lie group as their automorphism group has recently surged as an important problem in the study of general structure theory of algebras particle physics differential geometry and invariant system theory 2 4 11 14 17 191 since the automorphism group aut a of a real or complex algebra a is a lie group whose lie algebra is the derivation algebra der a of a zl 1 this is equivalent to the problem of classifying algebras having a given lie algebra as their derivation algebra symmetries that frequently appear in physics are represented by automorphisms of certain nonassociative algebras a where the largeness of aut a or der a reflects the symmetries such algebras with the symmetry group x 3 c su 3 or the compact exceptional lie group g2 have extensively been investigated in particle physics geometry of affrne connections on a reductive homogeneous space and for the study of nite dimensional real division algebras z 4 14 191 the color algebra of domokos and kiivesi domokos 4 o onion and para octonion algebras and the complex or real okubo algebra s are examples of such algebras a well known theorem of f adams asserts that if the sphere s admits

on algebras satisfying x 2x 2 n x x the commutative algebras satisfying the adjoint identity x 2x 2 n x x where n is a cubic form are shown to be related to a class of generically algebraic jordan algebras of degree at most 4 and to the pseudo composition algebras they are classified under a nondegeneracy condition

stability and bifurcation in a diffusive lotka volterra system with delay in this paper we investigate the dynamics of a class of diffusive lotka volterra equation with time delay subject to the homogeneous dirichlet boundary condition in a bounded domain the existence of spatially nonhomogeneous steady state solution is investigated by applying lyapunov schmidt reduction the stability and nonexistence of hopf bifurcation at the spatially nonhomogeneous steady state solution with the changes of a specific parameter are obtained by analyzing the distribution of the eigenvalues moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

periodicity in a nonlinear predator prey system on time scales with state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a nonlinear state dependent delays predator prey system on time scales

exponentially growing solutions for a delay diffusion equation with negative feedback abstract the scalar partial delay differential equation u t u u t 1 u t is investigated it was known that in one space dimension all nonnegative solutions of the initial boundary value problem stay bounded as t surprisingly this ceases to remain true in two or more dimensions if the delay is large and the diffusion coefficient small there exists a large set of trajectories whose total mass tends exponentially to infinity as t these trajectories escape the negative feedback of the equation by transporting their mass around along periodic paths in space where the paths can be prescribed by the initial data