multiple bifurcations in a delayed predator prey system with nonmonotonic functional response abstract a delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by faria and magalhaes the bifurcation analysis of the model indicates that there is a bogdanov takens singularity for any time delay value a versal unfolding of the model at the bogdanov takens singularity is obtained on the other hand it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit hopf bifurcation as the time delay passes through some critical values

stability and bifurcation for a delayed predator prey model and the effect of diffusion abstract we consider a predator prey system with one or two delays and a unique positive equilibrium e its dynamics are studied in terms of the local stability of e and of the description of the hopf bifurcation that is proven to exist as one of the delays taken as a parameter crosses some critical values we also consider a reaction diffusion system with neumann conditions resulting from adding one spatial variable and diffusion terms in the previous model the spectral and bifurcation analysis in the neighborhood of e now as a stationary point of this latter system is addressed and the results obtained for the case without diffusion are applied

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

global attractivity and positive almost periodic solution for delay logistic differential equation abstract in this paper we establish some sufficient conditions for the global attractivity of positive solutions and the unique existence of positive almost periodic solutions for delay logistic differential equations of the form x t r t x t a t b t x t l x t our results extend and improve corresponding ones in the literature

uniform persistence and global attractivity for nonautonomous competitive systems with nonlinear dispersion and delays in this paper we consider a nonautonomous lotka volterra competitive system with nonlinear discrete dispersion and a finite number of discrete delays the system which is consisted of two lotka volterra patches has two competitors one can disperse between two patches but the other is confined to one patch and cannot disperse our main focus is persistence i e the survival in two patches of the population and the existence of a periodic solution we also establish conditions under which the system admits a positive periodic solution which attracts all solutions

global stability of volterra models with time delay abstract easily verifiable conditions are obtained for the global stability of the positive steady state in volterra models with discrete and distributed time delays

global attractivity in delayed differential equations with applications to food limited population model abstract a new criterion is built which guarantees the global attractivity of zero solution for equation having the form x t 1 x t f t x t the behavior of global solution on r is also addressed as an application we study the existence of globally attractive positive almost periodic solution for the food limited single population model our results improve those in literature

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

dynamics of a discrete food limited population model with time delay abstract in this paper we consider a discrete food limited population model with time delay firstly the stability of the equilibrium of the system is investigated by analyzing the characteristic equation by choosing the time delay as a bifurcation parameter we prove that neimark sacker bifurcations occur when the delay passes a sequence of critical values then the explicit algorithm for determining the direction of the neimark sacker bifurcations and the stability of the bifurcating periodic solutions are derived finally some numerical simulations are given to verify the theoretical analysis

stability criteria for a system involving two time delays a system of two autonomous ordinary differential equations with two discrete time delays is considered with a view to determining the stability of equilibria using the nyquist criterion on the characteristic equation estimates on the length of delays are given for which a system which is stable in the absence of delays remains stable conditions are also derived for there to be no change in stability even for unbounded delays the above mentioned criteria are applied to a system modeling competitive interacting populations and to a predator prey system

harmless delays for uniform persistence abstract this paper studies a two dimensional predator prey system with a finite number of discrete delays our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system the results are obtained by constructing suitable persistence functionals

stability and hopf bifurcation in a delayed competition system abstract in this paper hopf bifurcation for two species lotka volterra competition systems with delay dependence is investigated by choosing the delay as a bifurcation parameter we prove that the system is stable over a range of the delay and beyond that it is unstable in the limit cycle form i e there are periodic solutions bifurcating out from the positive equilibrium our results show that a stable competition system can be destabilized by the introduction of a maturation delay parameter further an explicit algorithm for determining the direction of the hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the theory of normal forms and center manifolds and numerical simulations supporting the theoretical analysis are also given

persistence and stability of a stage structured predator prey model with time delays a delayed predator prey model with stage structure for the predator is proposed and investigated sufficient conditions are derived for persistence the local and global asymptotic stability of a positive equilibrium of the model numerical simulations are presented to illustrate the feasibility of our main results

the inductive blockwise alperin weight condition for g2 q and d43 q abstract the inductive blockwise alperin weight condition is a system of conditions whose verification for all non abelian finite simple groups would imply the blockwise alperin weight conjecture we establish this condition for the groups g 2 q q 5 and d 4 3 q for all primes dividing their order

dynamics of a competitive lotka volterra system with three delays abstract in this paper a competitive lotka volterra system with three delays is investigated by choosing the sum of three delays as a bifurcation parameter we show that in the above system hopf bifurcation at the positive equilibrium can occur as crosses some critical values and we obtain the formulae determining direction of hopf bifurcation and stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem finally numerical simulations supporting our theoretical results are also included

the dynamics of a piping system with internal unsteady flow abstract the dynamics of a pipeline conveying one dimensional unsteady flow is considered the dynamics of the fluid pipe system is represented by a set of partial differential equations which consists of the axial and transverse equations of motion of the pipeline and the equations of momentum and continuity of the internal flow the vibration equations of the pipeline are derived by use of newton s law of motion while the fluid equations are derived based on the concept of a deformable moving control volume the equations are fully coupled to each other and thus can be applied to various fluid pipe interaction problems which can be generated by the diverse operations of valves and pumps attached to the pipeline the equations are applied to a simply supported inclined straight pipeline to investigate the stabilities and dynamic responses of the pipeline the stability analysis is conducted by use of bolotin s method the dynamic responses are numerically investigated for both stable and unstable conditions it is observed that unstable regions in the stability chart expand as the flow velocity and the mass density of the fluid increase and that natural frequencies of the pipeline increase as the fluid friction acting on the inner surface of pipeline increases

global asymptotic stability beyond 3 2 type stability for a logistic equation with piecewise constant arguments abstract in this paper a logistic equation with multiple piecewise constant arguments is investigated in detail we generalize the approach in two papers k uesugi y muroya e ishiwata on the global attractivity for a logistic equation with piecewise constant arguments j math anal appl 294 2 2004 560 580 and y muroya e ishiwata n guglielmi global stability for nonlinear difference equations with variable coefficients j math anal appl 334 1 2007 232 247 and establish a new condition for the global stability of the equation their results are given as one of the special cases moreover we improve the 3 2 type stability condition under several dominance assumptions on the coefficients of the equation some examples and numerical simulations are also presented all of these examples show that there are several conditions for the global stability of the equation depending on the coefficients on the delay terms of the equation beyond the 3 2 type stability condition

vibration of a flexible pipe conveying viscous pulsating fluid flow abstract the non linear equations of motion of a flexible pipe conveying unsteadily flowing fluid are derived from the continuity and momentum equations of unsteady flow these partial differential equations are fully coupled through equilibrium of contact forces the normal compatibility of velocity at the fluid pipe interfaces and the conservation of mass and momentum of the transient fluid poisson coupling between the pipe wall and fluid is also incorporated in the model a combination of the finite difference method and the method of characteristics is employed to extract displacements hydrodynamic pressure and flow velocities from the equations a numerical example of a pipeline conveying fluid with a pulsating flow is given and discussed

stability of a competition model with two stage structure a population model with stage structure which describes the competition of two species for space is considered the model is established under the assumptions that reproductive rates of two species are affected by competition and that the space occupied by one type of juveniles cannot be neglected estimates on the length of delays for which positive equilibrium of the model remains stable are given sufficient conditions are also derived that ensure global stability of positive equilibrium

irreducible restrictions of brauer characters of the chevalley group g2 q to its proper subgroups let g2 q be the chevalley group of type g2 defined over a finite field with q pn elements where p is a prime number and n is a positive integer in this paper we determine when the restriction of an absolutely irreducible representation of g in characteristic other than p to a maximal subgroup of g2 q is still irreducible similar results are obtained for b22 q and g22 q

global stability for a class of nonlinear nonautonomous delay equations it is easy to imagine that more realistic models for single species growths should take into account both the changing of the environment and the effects of time delay thus it is neces sary and interesting to study the following general nonlinear nonautonomous delay equation x t l x t i s

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

on quotients of hom functors and representations of finite general linear groups i abstract this is a second article on quotients of hom functors and their applications to the representation theory of finite general linear groups in a nondescribing characteristic after some general results on quotients of hom functors and their connection to the harish chandra theory these constructions are used to obtain a full classification of the l modular irreducible representations of gl n q for some prime power q which is not divisible by the prime l and to explain some facts on their harish chandra series and decomposition numbers

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

global attractivity in scalar delayed differential equations with applications to population models for the scalar delay differential equation x t 1 x t f t xt sufficient conditions for the global stability of the zero solution are given the behavior of global solutions on r is also addressed several applications to population models which improve known results are presented

a study on the dynamic stability of a cylindrical shell conveying a pulsatile flow of hot fluid abstract the flow of hot fluid having a harmonic component superposed on the mean flow velocity is considered flowing through an insulated cylindrical shell the cylindrical shell will be subjected to thermal load due to the flow of hot fluid the semi analytical finite element forms the basis for modelling the structural continuum under the influence of temperature and the flowing fluid the fluid flowing through the cylindrical shell is incompressible and linear potential flow theory is used to formulate the fluid domain bernoulli s principle and impermeability conditions of the fluid are the basis for a coupled fluid structure interaction analysis model reduction technique in conjunction with the fourth order runge kutta method using gill s coefficient is adopted to compute the state transition matrix which provides the stability information of the periodic system the results of the theoretical studies are presented related to instability regions due to a pulsatile flow of hot fluid through a cylindrical shell hot fluid at various magnitude of constant temperature limited by the critical thermal buckling temperature is considered in the study the effect of fluid temperature and excitation parameter on the behavior of dynamic instability of the system is examined

existence and dynamics of quasilinear parabolic systems with time delays abstract this paper is concerned with a coupled system of quasilinear parabolic equations where the effect of time delays is taken into consideration in the reaction functions of the system the partial differential operators in the system may be degenerate and the reaction functions possess some mixed quasimonotone property including quasimonotone nondecreasing functions the aim of the paper is to show the existence and uniqueness of a global solution to the parabolic system the existence of positive quasisolutions or maximal minimal solutions of the corresponding elliptic system and the asymptotic behavior of the solution of the parabolic system in relation to the quasisolutions or maximal minimal solutions of the elliptic system applications are given to three reaction diffusion models arising from mathematical biology and ecology where the diffusion coefficients are density dependent and are degenerate this degenerate density dependent diffusion leads to some interesting distinct asymptotic behavior of the time dependent solution when compared with density independent diffusion

exponential stability of a competitive lotka volterra system with delays abstract in this paper the exponential stability of a two species competitive lotka volterra system with discrete delays has been studied by constructing appropriate lyapunov functional and using the linear matrix inequality lmi optimization approach a series of sufficient criteria is obtained which ensure the exponential stability of the positive equilibrium of the given lotka volterra system the results are new and improve some earlier work an illustrative example is given to demonstrate the effectiveness of the obtained results

a note on delay independent stability of a predator prey model abstract this paper analyzes the delay independent stability of a predator prey model with the assistance of the delay independent stability criteria for a class of retarded dynamical systems an interesting result is obtained that the delay independent stability condition is equivalent to the zero delay stability condition in this model the physical meaning of this result is also given

reaction diffusion systems with time delays monotonicity invariance comparison and convergence in a recent paper we have obtained differential inequality results developed comparison theorems and established invariance criteria for mild solutions of abstract functional differential equations in a banach space the primary application for these results is to reaction diffusion systems in which the reaction nonlinearity contains time delays in the present paper we apply these results to reaction diffusion systems with time delays of the form u t d u f x u t x x u u n 0 x where is a bounded open set in r n with smooth boundary u r n d diag d 1 d n with d i 0

motion of a moving elastic beam carrying a moving mass analysis and experimental verification abstract in this paper vibrational motion of an elastic beam fixed on a moving cart and carrying a moving mass is investigated the equations of motion of the beam mass cart system are derived and the coupled dynamic equations are solved by the unconstrained modal analysis in modal analysis the exact normal mode solutions corresponding to the eigenfrequencies for each position of the moving mass and the ratios of the weight of the beam mass cart system are used proper transformation of time solutions between the normal modes for a position and those for the next position of the moving mass is also considered numerical simulations are carried out to obtain open loop responses of the system in tracking pre designed paths of the moving mass the simulation results show that the model predicts the dynamic behavior of the beam mass cart system well experiments are carried out to show the validity of the proposed analytical method

conditions for preservation of stability of adaptive controllers for systems with unmodeled delay some recent results from the mathematical literature are used to derive conditions under which stability of an adaptive controlled system first order plant with output feedback is preserved in spite of the presence of a time delay in the plant input bounds on the delay for which stability is preserved are derived for three robust versions of the gradient update law fixed sigma modification with and without normalization and a time varying sigma modification

in plane and out of plane motions of an extensible semi circular pipe conveying fluid abstract in plane and out of plane motions of a semi circular pipe conveying fluid are analyzed in this paper assuming that the centerline of the semi circular pipe is extensible nonlinear equations of in plane and out of plane motions are derived according to the extended hamilton principle the lagrange nonlinear strain theory and the euler bernoulli beam theory are used to derive the equations the derived equations of motion are discretized by applying the galerkin method linearized equations around the equilibrium position are obtained from the discretized equations and then the dynamic characteristics of the pipe are investigated in addition some modelling issues which are related to the nonlinearity of the circumferential strain and stress are discussed this study finds that a semi circular pipe conveying fluid does not lose stability even at a high fluid velocity although a model using the lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies a model using the lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy

global stability for separable nonlinear delay differential systems abstract in this paper we consider separable nonlinear delay differential systems and we establish conditions for global asymptotic stability of the zero solution applying these we offer improved 3 2 type criteria for global asymptotic stability of nonautonomous lotka volterra systems with delays

2 blocks and 2 modular characters of the chevalley groups we first determine the distribution of the ordinary irreducible characters of the exceptional chevalley group g2 q q odd into 2 blocks this is done by using the method of central characters then all but two of the irreducible 2 modular characters are determined the results are given in the form of decomposition matrices the methods here involve concepts from modular representation theory and symbolic computations with the computer algebra system maple as a corollary the smallest degree of a faithful representation of g2 q q odd over a field of characteristic 2 is obtained

robust interval stability persistence and partial stability on lotka volterra systems with time delay abstract lotka volterra ecological systems with discrete time delays are studied where the information about the biological vital parameters such as the rates of birth death and interaction between species is incomplete but their upper and lower bounds are known by using stability theory of the interval dynamical systems and constructing suitable liapunov functionals robust stability partial robust stability and robust persistence of those lotka volterra systems are investigated and sufficient conditions are obtained respectively

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

global stability for separable nonlinear delay differential equations consider the following separable nonlinear delay differential equation dy t dt i 0ma i t g i y t i t t t 0y t f t t t 0 where we assume that there is a strictly monotone increasing function f x on such that f 0 0 00 0 i m andiff x x thenlim x f x orlim x f x isfinite in this paper to the above separable nonlinear delay differential equation we establish conditions of global asymptotic stability for the zero solution in particular for a special wide class of f x which contains a case of f x e x 1 we give more explicit conditions applying these we offer conditions of global asymptotic stability for solutions of nonautonomous logistic equations with delays

global attractivity and positive almost periodic solution of a single species population model abstract 3 2 criterion is built which guarantees the global attractivity of positive solution for equation having the form x t a t x t 1 l t x t where a t 0 and the linear functional l t is positive moreover when the equation is almost periodic the similar conditions can also guarantee the existence and uniqueness of almost periodic solution that is globally attractive our results improve those in literature

new non linear modelling for vibration analysis of a straight pipe conveying fluid abstract a new non linear model of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends using the euler bernoulli beam theory and the non linear lagrange strain theory from the extended hamilton s principle the coupled non linear equations of motion for the longitudinal and transverse displacements are derived these equations of motion are discretized by using the galerkin method after the discretized equations are linearized in the neighbourhood of the equilibrium position the natural frequencies are computed from the linearized equations on the other hand the time histories for the displacements are also obtained by applying the generalized time integration method to the non linear discretized equations the validity of the new modelling is provided by comparing results from the proposed non linear equations with those from the equations proposed by paidoussis

uno s invariant conjecture for chevalley groups g2 q in nondefining characteristics abstract uno s invariant conjecture for the chevalley groups g 2 q has been verified when the characteristic of the modular representation is distinct from the defining characteristic of the groups thus dade s reductive conjecture and the isaacs navarro conjecture both hold for g 2 q in non defining characteristics

on the number of simple modules in a block of a finite group abstract we prove that if b is a p block with non trivial defect group d of a finite p solvable group g then l b p r where r is the sectional rank of d we remark that there are infinitely many p blocks b with non abelian defect groups and l b p r 1 we conjecture that the inequality l b p r holds for an arbitrary p block with defect group of sectional rank r we show this to hold for a large class of p blocks of various families of quasi simple and nearly simple groups

a discrete periodic lotka volterra system with delays in this paper we investigate the following discrete periodic lotka volterra system with delays x n 1 x n expb n i 1qai n x n ti j 1mcj n y n li y n 1 y n expr n i 1qdi n x n ki j 1mej n y n si the sufficient and realistic conditions are obtained for the existence of positive periodic solutions and the permanence for the above system

brauer trees for blocks of cyclic defect in the groups g2 q for primes dividing q2 q 1 1 are dealt with in sl 1 where we also describe the blocks of noncyclic defect for these primes these results form part of a project proposed by walter feit namely to determine the brauer trees for all finite groups the blocks and brauer trees for the groups g 2k and g2 3k are described in s2 and a survey of all the results in this paper and in sl sz is given in s3 the conjugacy classes and character tables for

permanence extinction and balancing survival in nonautonomous lotka volterra system with delays in this paper the periodic n species lotka volterra competition systems with time delays are considered the sufficient conditions are derived for the permanence extinction and balancing survival of the system some known results are improved and unified further our results suggest that under some conditions the introduction and the variance of the time delays will be either harmless or useless conjecture about the effect of time delays on some global behaviors of the system is advanced

3 2 type criteria for global attractivity of lotka volterra competition system without instantaneous negative feedbacks this paper deals with a two species lotka volterra competition model with discrete delays but without instantaneous negative feedbacks motivated by wright s 3 2 global attractivity result for the delayed scalar logistic equation we establish some new 3 type criteria for global attractivity of the positive equilibrium of the system these criteria provide convenient and better than some existing estimates for the diagonal delays

stability and bifurcation analysis for a delayed lotka volterra predator prey system the present paper deals with a delayed lotka volterra predator prey system by linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation we find the necessary conditions that the parameters should verify in order to have the oscillations in the system in addition the normal form of the hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these hopf bifurcations to verify the obtained conditions a special numerical example is also included

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 non autonomous lotka volterra competition system without instantaneous negative feedback abstract we consider a non autonomous lotka volterra competition system with distributed delays but without instantaneous negative feedbacks i e pure delay systems we establish some 3 2 type and m matrix type criteria for global attractivity of the positive equilibrium of the system which generalise and improve the existing ones

global attractivity for a delay logistic equation with instantaneous terms abstract in this paper some global attractivity conditions are obtained for delay logistic differential equation with instantaneous terms x t r t 1 x t cx t f t x t t 0 where c 0 these conditions extend and improve all existing relative results in literature

local and global stability for lotka volterra systems with distributed delays and instantaneous negative feedbacks abstract this paper addresses the local and global stability of n dimensional lotka volterra systems with distributed delays and instantaneous negative feedbacks necessary and sufficient conditions for local stability independent of the choice of the delay functions are given by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect the global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability for the case of monotone interactions however sharper conditions are presented this paper generalizes known results for discrete delays to systems with distributed delays several applications illustrate the results

new conditions on the existence and stability of periodic solution in lotka volterra s population system in this paper we revisit the famous periodic lotka volterra competitive system some new and interesting sufficient conditions are obtained to guarantee the existence and global asymptotic stability of the periodic solution in the lotka volterra competitive system our method is based on mawhin s coincidence degree matrix s spectral theory and some new estimation techniques for the priori bounds of unknown solutions to the equation lx lambda nx due to this new method our new results are much different from the known results in the previous literature finally some examples and their simulations show the feasibility of our results

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

isometries and extra special sylow groups of order p3 abstract a new type of isometry between the sets of irreducible characters of blocks is introduced and a conjecture is stated using the classifications of finite simple groups and saturated fusion systems over an extra special group p of order p 3 and exponent p we check that the conjecture is affirmatively answered for the principal blocks of finite groups with sylow p subgroup p

cross diffusion induced turing instability for a competition model with saturation effect abstract competitive behavior like predation widely exists in the world which has influences on the dynamics of ecosystems though a good knowledge for the patten formation and selection of predator prey models with diffusion is known in the literature little is known for that of a diffused competition model as a result a competition model with saturation effect and self and cross diffusion is proposed and analyzed in this paper firstly by making use of nullcline analysis we derive the condition of existence and stability of positive equilibrium and prove global stability then using the linear stability analysis the turing bifurcation critical value and the condition of the occurrence of turing pattern are obtained when control parameter is selected finally we deduce the amplitude equations around the turing bifurcation point by using the standard multiple scale analysis meanwhile a series of numerical simulations are given to expand our theoretical analysis this work shows that cross diffusion plays a key role in the formation of spatial patterns for competitive model with saturation effect

on a delay differential equation for single specie population variations on considere l equation differentielle scalaire a retard n t n t a bn t n t 1 on suppose a b constantes positives et on etudie les solutions pour t 0 telles que n t n 0 t 1 t 0 avec n 0 t une fonction initiale donnee positive et continue on obtient des resultats sur la limitation et le comportement asymptotique des solutions

a global stability criterion in nonautonomous delay differential equations abstract consider the following nonautonomous nonlinear delay differential equation d y t d t a t y t i 0 m a i t g i y i t t t 0 y t t t t 0 where we assume that there is a strictly monotone increasing function f x on such that f 0 0 0 g i x f x 1 x 0 0 i m and if f x x then lim x f x or lim x f x is finite in this paper to the above nonautonomous nonlinear delay differential equation we establish conditions of global asymptotic stability for the zero solution in particular for a special wide class of f x which contains two cases f x e x 1 and f x x we give more explicit conditions which are some extension of the 3 2 type criterion applying these to discrete models of nonautonomous delay differential equations we also obtain new sufficient conditions of the global asymptotic stability of the zero solution

global stability in delay differential systems without dominating instantaneous negative feedbacks abstract most of the global stability or convergence results appearing so far for delayed lotka volterra type systems or other delay differential systems require that the instantaneous negative feedbacks dominate both delayed feedback and interspecific interactions such a requirement is rarely met in real systems since feedbacks are generally delayed this leads to the long standing question under what conditions will the global stability of a nonnegative steady state of a differential delay system persist when time delays involved in some part of the negative feedbacks are small enough this paper presents a partial answer to this open question roughly our results show that if the delay differential system remains dissipative when delays are introduced then the above open question has an affirmative answer our results also improve some recent findings

degenerate lyapunov functionals of a well known prey predator model with discrete delays it is commonly believed that as far as stabilities are concerned small delays are negligible in some modelling processes however to have an affirmative answerfor this common belief is still an open problem for many nonlinear equations in this paper the classical lotka volterra prey predator equation with discrete delays is considered and by using degenerate lyapunov functionals method an affirmative answer to this open problem on both local and global stabilities of the prey predator delay equations is given it is shown that degenerate lyapunov functional method is a powerful tool for studying the stability of such nonlinear delay systems a detailed and explicit procedure of constructing such functionals is provided furthermore some explicit estimates on the allowable sizes of the delays are obtained