positive solutions of periodic boundary value problems for nonlinear first order impulsive differential equations abstract motivated by liu y liu further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations j math anal appl 327 2007 435 452 li et al x li x lin d jiang x zhang existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects nonlinear anal 62 2005 683 701 and liu and ge y liu w ge stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients nonlinear anal 57 2004 363 399 this paper is concerned with the periodic boundary value problem pbvp for short for the nonlinear impulsive differential equation x t a t x t f t x t a e t 0 t t 1 t p x t k x t k x t k i k x t k k 1 p x t x 0 we obtain new sufficient conditions for the existence of at least one two or three positive solutions of the above pbvp respectively examples are presented to illustrate the main results

asymptotically periodic solutions of n competing species problem with time delays abstract a general nonautonomous lotka volterra system of integro differential equations with infinite delay is considered and sufficient conditions for uniform stability and asymptotic stability of solutions are investigated these limiting equations are used to obtain the existence of asymptotically periodic solutions of the corresponding system of equations where lower limit in the integration is zero

periodic solutions for a neutral nonlinear dynamical equation on a time scale abstract let t be a periodic time scale we use a fixed point theorem due to krasnosel ski to show that the nonlinear neutral dynamic system with delay x t a t x t c t x t k q t x t x t k t t has a periodic solution we assume that k is a fixed constant if t r and is a multiple of the period of t if t r under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle

existence and exponential stability of piecewise mean square almost periodic solutions for impulsive stochastic nicholson s blowflies model on time scales the concept of piecewise mean square almost periodic stochastic process is introduced a new impulsive stochastic nicholsons blowflies model is introduced and studied on time scales the first results of the piecewise mean square almost periodic solutions for the model are obtained in this paper a class of impulsive stochastic nicholson s blowflies model with patch structure and nonlinear harvesting terms is introduced and studied on time scales by using contraction mapping principal and gronwall bellman inequality technique some sufficient conditions for the existence and exponential stability of piecewise mean square almost periodic solutions for the model with infinite delays are established on time scales finally an example is given to demonstrate the validity of the conditions of the main theorem

analysis of a nonautonomous nicholson blowfly model abstract most dynamic models describing population evolution contain one or more parameters the parameters are treated as fixed constants and qualitative results such as stability of equilibria are calculated using this assumption in reality however the parameters are mathematically evaluated by statistical methods in which the error is decreased over a number of calculations therefore the parameter is a sequence converging to the actual parameter value as time goes to infinity in this article we consider the k th order discrete nicholson blowfly model n n 1 f p n n n n k where and p are parameters for a particular range of parameter values global stability results are well known the general form of the discrete dynamical system is now rewritten as n n 1 f p n n n n n n k where p n and n converge to the parametric values p and we show that when the parameters are replaced by sequences the stability results of the original system still hold this technique may be of general interest to those studying evolutionary systems in which the parameters are not fundamental constants but sequences

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

existence results for abstract impulsive second order neutral functional differential equations abstract we establish the existence of mild solutions for a class of impulsive second order partial neutral functional differential equations with infinite delay in a banach space

mean square almost periodic solution for impulsive stochastic nicholson s blowflies model with delays in this paper a class of impulsive stochastic nicholson s blowflies model is investigated by applying cauchy matrix under proper conditions the existence and exponential stability of square mean almost periodic solutions for the model with multiple nonlinear harvesting terms and delays moreover an example is provided to illustrate the effectiveness of the results

oscillation of continuous and discrete diffusive delay nicholson s blowflies models in this paper we consider the continuous and the discrete delay diffusive nicholson s blowflies models with different types of boundary conditions our aim is to give some sufficient conditions for oscillation of all positive solutions about the positive steady state we show that these conditions have essentially first order character by reducing the problem of oscillation of the boundary value problem to that of first order delay differential or difference equation

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

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

hopf bifurcation analysis in a delayed nicholson blowflies equation abstract the dynamics of a nicholson s blowflies equation with a finite delay are investigated we prove that a sequence of hopf bifurcations occur at the positive equilibrium as the delay increases explicit algorithm for determining the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions are derived using the theory of normal form and center manifold global existence of periodic solutions are established using a global hopf bifurcation result of wu trans amer math soc 350 1998 4799 and a bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney j differential equations 106 1994 27

strongly damped wave equation in uniform spaces abstract the cauchy problem for a semilinear strongly damped wave equation is considered in the whole of r n under suitable conditions imposed on nonlinear term which are much like for equations in bounded domains a dissipative semigroup t t of global solutions to this problem is constructed in a reach phase space being the product of the locally uniform spaces existence of an attractor for t t is then established

asymptotic behavior of solutions for initial boundary value problems for strongly damped nonlinear wave equations abstract we study initial boundary value problems for strongly damped nonlinear wave equations by using improved integral estimates it is proven that the solutions of the problems decay to zero exponentially as time t approaches infinity under a very simple and general assumption regarding the nonlinear term

dynamics of multi species competition predator system with impulsive perturbations and holling type iii functional responses abstract we investigate the dynamics of a class of multi species predator prey interaction models with holling type iii functional responses based on systems of nonautonomous differential equations with impulsive perturbations sufficient conditions for existence of a positive periodic solution are investigated by using a continuation theorem in coincidence degree theory which have been extensively applied in studying existence problems in differential equations and difference equations in addition sufficient criteria are established for the global stability and the globally exponential stability of the system by using the comparison principle and the lyapunov method

existence and global attractivity of positive periodic solutions for the impulsive delay nicholson s blowflies model in this paper we shall consider the following nonlinear impulsive delay population model 0 1 x t d t x t p t x t m w e a t x t m w a e t 0 t t k x t k 1 b k x t k k 1 2 where m is a positive integer d t a t and p t are positive periodic continuous functions with period w 0 in the nondelay case m 0 we show that 0 1 has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate linear periodic impulsive perturbations the impulsive delay equation 0 1 preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

global exponential stability of positive periodic solutions for a delayed nicholsonʼs blowflies model abstract this paper is concerned with a non autonomous delayed nicholson s blowflies model under proper conditions we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions this answers an open problem proposed by berezansky et al 2010 2 we also provide numerical simulations to support the theoretical result

almost periodic solutions of lasota wazewska type delay differential equation sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a single species model given by the nonautonomous lasota wazewska type delay differential equations x t txt ptfxt in which 0 p t 0 t are continuous almost periodic functions and f is a decreasing positive c1 function conditions of the uniform asymptotical stability for some associated nonautonomous delay differential equations x t txt ptxt are also discussed

existence of positive periodic solutions for a generalized nicholson s blowflies model in this paper by using the krasnoselskii cone fixed point theorem we obtain a sufficient condition as well as a necessary condition for the existence of positive periodic solutions of the following generalized nicholson s blowflies model x t d t x t i 1mp i t x t t i t e q i t x t t i t t 0 in the degenerate case i e where the coefficients and delays of the above equation are all constants a sufficient and necessary condition for the existence of positive periodic solutions is obtained our results are completely new and generalize and improve some results from the literature

on the stability and uniform persistence of a discrete model of nicholson s blowflies abstract consider the delay difference equation n n 1 nn n n pn n k e an n k n 0 1 2 1 which is a discrete analogue of the delay differential equation n t n t pn t e an t t 0 cf 8 we show that when p the zero solution of 1 is uniformly asymptotically stable and every non negative solution of 1 tends to zero as n while for p 1 is uniformly persistent moreover if in addition to p we also have 1 k 1 1 ln p 1 then every positive solution of 1 tends to the positive equilibrium n 1 a ln p

almost periodic solutions for abstract impulsive differential equations this paper studies the existence and uniqueness of exponentially stable almost periodic solutions for abstract impulsive differential equations in banach space the investigations are carried out by means of the fractional powers of operators we construct an example to illustrate the feasibility of our results

on a stochastic logistic equation with impulsive perturbations a stochastic logistic model with impulsive perturbations is proposed and investigated first we give a new definition of a solution of an impulsive stochastic differential equation isde which is more convenient for use than the existing one using this definition we show that our model has a global and positive solution and obtain its explicit expression then we establish the sufficient conditions for extinction non persistence in the mean weak persistence persistence in the mean and stochastic permanence of the solution the critical value between weak persistence and extinction is obtained in addition the limit of the average in time of the sample path of the solution is estimated by two constants afterwards the lower growth rate and the upper growth rate of the solution are estimated finally sufficient conditions for global attractivity are established

a new approach for positive almost periodic solutions to a class of nicholson s blowflies model this paper is concerned with the existence of almost periodic solutions for a class of nicholson s blowflies model by transforming the model into an equivalent integral equation and using a fixed point theorem in cones we establish a new result about the existence of positive almost periodic solutions for the model comparing with some earlier works on almost periodic solutions for nicholson s blowflies models our approach is novel

global attractivity in population dynamics we established sufficient conditions for the global attractivity of the positive equilibrium of the delay differential equation n t mu n t i 1m pi exp n t i t 0 m 1 for m 1 equation 1 was used by wazewska czyzewska and lasota as a model for the survival of red blood cells in an animal

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

computation of invariant tori by the method of characteristics in this paper we present a technique for the numerical approximation of a branch of invariant tori of finite dimensional ordinary differential equations systems our approach is a discrete version of the graph transform technique used in analytical work by fenichel indiana univ math j 21 1971 pp 193 226 in contrast to our previous work l dieci j lorenz and r d russell siam j sci statist comput 12 1991 pp 607 647 the method presented here does not require a priori knowledge of a suitable coordinate system for the branch of invariant tori but determines and updates such a coordinate system during a continuation process we give general convergence results for the method and present its algorithmic description we also show how the method performs on two physically important nonlinear problems a system of two coupled oscillators and the forced van der pol oscillator in the latter case we discuss some modifications needed to approximate an invariant curve for the poincare map

nonexistence of global solutions to semilinear wave equations in high dimensions on considere le probleme de cauchy pour l equation d onde semi lineaire 2 t 2 u x t u x t p p 1 u x o f x u t x o g x avec f g c o r n

asymptotic stability of competitive systems with delays and impulsive perturbations abstract a general impulsive nonautonomous lotka volterra system of integro differential equations with infinite delay is considered the impulses are realized at fixed moments of time sufficient conditions for uniform stability and asymptotic stability of solutions are investigated the main results are obtained by using the comparison principle and the lyapunov method

the existence of positive almost periodic type solutions for some neutral nonlinear integral equation abstract this paper presents the conditions of existence of positive almost periodic type solutions for some neutral nonlinear integral equation by using a fixed point theorem in the cone some known results are extended

existence of periodic solution of order one of planar impulsive autonomous system based on the situation that all the recent research about state dependent impulsive differential equations is focused on systems which have explicit solutions this paper try to consider those systems with state dependent impulsion which have not explicit solutions we get an existence theorem of periodic solution of order one for a general planar autonomous impulsive system and by applying it to a special state dependent impulsive differential equations we get the concrete conditions of existence of one order periodic solution of that special system

global existence of weak solutions for two dimensional semilinear wave equations with strong damping in an exterior domain abstract we consider two dimensional mixed problems in an exterior domain for a semilinear strongly damped wave equation with a power type nonlinearity u p if the initial data have a small weighted energy we shall derive a global existence and energy decay results in the case when the power p of the nonlinear term satisfies p 6

positive almost periodic solution for a class of nicholson s blowflies model with multiple time varying delays in this paper we study the existence and exponential convergence of positive almost periodic solutions for the generalized nicholson s blowflies model with multiple time varying delays under proper conditions we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution moreover we give some examples to illustrate our main results

permanence and global stability for nonautonomous n species lotka volterra competitive system with impulses and infinite delays abstract in this paper we consider a class of nonautonomous n species lotka volterra competitive systems with impulses and infinite delays by developing the methods given in teng 2002 25 we give sufficient conditions for permanence and global attractivity of the system

global existence and exponential stability of small solutions to nonlinear viscoelasticity the global existence of smooth solutions to the equations of nonlinear hyperbolic system of 2nd order with third order viscosity is shown for small and smooth initial data in a bounded domain ofn dimensional euclidean space with smooth boundary dirichlet boundary condition is studied and the asymptotic behaviour of exponential decay type of solutions ast tending to is described time periodic solutions are also studied as an application of our main theorem nonlinear viscoelasticity strongly damped nonlinear wave equation and acoustic wave equation in viscous conducting fluid are treated

positive almost periodic solution for a class of lasota wazewska model with multiple time varying delays in this paper we study the existence and global exponential convergence of positive almost periodic solutions for the generalized lasota wazewska model with multiple time varying delays under proper conditions we employ a novel proof to establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution moreover we give an example to illustrate our main results

energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations we derive the total energy decay e t leq i 0 1 t 1 and l 2 boundedness u t 2 leq ci 0 for the solutions to the initial boundary value problem for the wave equation in an exterior domain omega u tt delta u a x u t 0 mbox in omega times 0 infty with u x 0 u 0 x u t x 0 u 1 x mbox and u partial omega 0 where i 0 u 0 h 1 u 1 2 and a x is a nonnegative function which is positive near some part of the boundary partial omega and near infinity we apply these estimates to prove the global existence of decaying solutions for semilinear wave equations with nonlinearity f u like u alpha u alpha 0 we note that no geometrical condition is imposed on the boundary partial omega

efficient numerical path following beyond critical points the paper presents a numerical pathfollowing technique based on an implicit change of parametrization using qr decomposition an automatic steplength control for tangent continuation is derived on a theoretical basis in the suggested approach turning points do not play any exceptional role for the actual computation of simple bifurcation points a special algorithm based on the augmented system of moore is developed this treatment includes imperfect bifurcations and permits an easy way of branch switching an efficient linear equation solver is worked out in connection with the qr decomposition finally numerical comparisons are included that clearly document the efficiency of the newly developed algorithms

some results on boundary value problems for fuzzy differential equations with functional dependence abstract we calculate the exact solution for a class of boundary value problems for first order linear fuzzy differential equations with impulses under hukuhara differentiability by finding green s function some conclusions can be derived for impulsive fuzzy differential equations including a term with functional dependence for which existence and uniqueness results are proved

lyapunov method for boundedness of solutions of nonlinear impulsive functional differential equations sufficient conditions are investigated for boundedness of solutions of nonlinear impulsive functional differential equations with impulses at fixed moments the main tools are lyapunov functions and gronwall type of inequality

perron s theorem for linear impulsive differential equations with distributed delay in this paper it is shown that under a perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable

adaptive data distribution for concurrent continuation continuation methods compute paths of solutions of nonlinear equations that depend on a parameter this paper examines some aspects of the multicomputer implementation of such methods the computations are done on a mesh connected multicomputer with 64 nodes one of the main issues in the development of concurrent programs is load balancing achieved here by using appropriate data distributions in the continuation process many linear systems have to be solved for nearby points along the solution path the corresponding system matrices are closely related to each other therefore pivots which are good for thelu decomposition of one matrix are likely to be acceptable for a whole segment of the solution path this suggests to choose certain data distributions that achieve good load balancing in addition if these distributions are used the resulting code is easily vectorized to test this technique the invariant manifold of a system of two identical nonlinear oscillators is computed as a function of the coupling between them this invariant manifold is determined by the solution of a system of nonlinear partial differential equations that depends on the coupling parameter a symmetry in the problem reduces this system to one single equation which is discretized by finite differences the solution of the discrete nonlinear system is followed as the coupling parameter is changed

global positive periodic solutions of periodic n species competition systems abstract in this paper an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized n species lotka volterra type and gilpin ayala type competition systems is obtained it improves a series of the well known sufficiency theorems in the literature about the problems mentioned above the method is based on a well known fixed point theorem in a cone of banach space this approach can be applied to more general competition systems

positive almost periodic solution for a class of lasota wazewska model with infinite delays abstract by utilizing a fixed theorem in cones we study the existence of a unique positive almost periodic solution for a generalized lasota wazewska model with infinite delays some sufficient conditions which ensure the existence of a unique positive almost periodic solution are derived and it cannot be obtained by the contraction mapping principle furthermore under proper conditions we establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution an example is provided to illustrate the effectiveness of the proposed result

an analytical and numerical study of the bifurcations in a system of linearly coupled oscillators abstract we study a two parameter family of ordinary differential equations in r 4 that governs the dynamics of two coupled planar oscillators each oscillator has a unique periodic solution that is attracting and the uncoupled product system has a unique invariant torus that is attracting the torus persists for weak coupling and contains two periodic solutions when the coupling is linear and conservative one of these in which the oscillators are synchronized persists and is stable for all coupling strengths the other in which the oscillators are radiant out of phase disappears either in a hopf bifurcation or when fixed points appear on the orbit at a critical ratio of the coupling strength to the frequency the out of phase oscillation is unstable except on an open set in the frequency coupling strength plane which contains moderate values of both parameters furthermore there are tori bifurcating from the out of phase solution which means according to the arnol d theory for hopf bifurcations in maps that there may be periodic solutions of arbitrarily large period and chaotic solutions as well numerous other bifurcations occur and there are a number of higher codimension singularities in a large region of the frequency coupling parameter plane stable steady states coexist with stable periodic solutions

strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation the aim of this article is twofold first we consider the wave equation in the hyperbolic space hi and obtain the counterparts of the strichartz type estimates in this context next we examine the relationship between semilinear hyperbolic equations in the minkowski space and in the hyperbolic space this leads to a simple proof of the recent result of georgiev lindblad and sogge on global existence for solutions to semilinear hyperbolic problems with small data shifting the space time strichartz estimates from the hyperbolic space to the minkowski space yields weighted strichartz estimates in rn x 1r which extend the ones of georgiev lindblad and sogge

existence and stability of periodic solution of a lotka volterra predator prey model with state dependent impulsive effects according to biological and chemical control strategy for pest we investigate the dynamic behavior of a lotka volterra predator prey state dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds by using poincare map and the properties of the lambert w function we prove that the sufficient conditions for the existence and stability of semi trivial solution and positive periodic solution numerical simulations are carried out to illustrate the feasibility of our main results

on almost periodic processes in uncertain impulsive delay models of price fluctuations in commodity markets we present an impulsive price model for a single commodity market with delays and uncertain terms impulsive perturbations are realized at fixed moments of time and are proposed to model price shocks in the case of continuous time representation to do so the paper resorts to the theory of impulsive differential equations uncertain terms are due to modeling errors measurement inaccuracy mutations in the fluctuation processes and so on we investigate conditions under which the extended model is capable of generating a stable almost periodic process

existence and global attractivity of unique positive periodic solution for a lasota wazewska model abstract in this paper we consider the lasota wazewska model x t a t x t i 1 m p i t e q i t x t i t by using a fixed point theorem some criteria are established for the existence of the unique positive periodic solution x of the above equation in particular we not only give the conclusion of convergence of x n to x where x n is a successive sequence but also show that x is a global attractor of all other positive solutions

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

partial persistence and extinction in n dimensional competitive systems abstract in this paper we first consider an n dimensional system slightly more general than the lotka volterra system and give conditions that imply strong persistence of all species using this result we then give computable conditions on the coefficients which imply the ultimate extinction of certain species in an n dimensional lotka volterra system

almost periodic solutions of neutral functional differential equations in this paper we study a non autonomous neutral functional differential equation in a banach space applying the theory of semigroups of operators to evolution equations and krasnoselskii s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under consideration

cauchy problem for quasi linear wave equations with nonlinear damping and source terms abstract the paper studies the existence and non existence of global weak solutions to the cauchy problem for a class of quasi linear wave equations with nonlinear damping and source terms it proves that when max m p where m 1 1 and p 1 are respectively the growth orders of the nonlinear strain terms the nonlinear damping term and the source term under rather mild conditions on initial data the cauchy problem admits a global weak solution especially in the case of space dimension n 1 the weak solutions are regularized and so generalized and classical solution both prove to be unique on the other hand if 0 1 and the initial energy is negative then under certain opposite conditions any weak solution of the cauchy problem blows up in finite time and an example is shown

periodicity on a class of neutral impulsive delay system we present some sufficient conditions for the existence of positive periodic solutions of a class of neutral impulsive delay differential system when our results applied to the differential system without impulse a known result in the literature is corrected moreover one example is given to illustrate the results obtained

global attractivity of the almost periodic solution of a delay logistic population model with impulses in this paper we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations by using a comparison theorem and constructing a suitable lyapunov functional a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained as applications some special models are studied our new results improve and generalize former results

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

second method of lyapunov and existence of integral manifolds for impulsive differential difference equations by means of piecewise continuous functions which are analogues of lyapunov s functions sufficient conditions are obtained for the existence of integral manifolds for impulsive differential difference equations with variable impulsive perturbations

global attractivity and permanence of a sveir epidemic model with pulse vaccination and time delay in this study we propose a new sveir epidemic disease model with time delay and analyze the dynamic behavior of the model under pulse vaccination pulse vaccination is an effective strategy for the elimination of infectious disease using the discrete dynamical system determined by the stroboscopic map we obtain an infection free periodic solution we also show that the infection free periodic solution is globally attractive when some parameters of the model under appropriate conditions the permanence of the model is investigated analytically our results indicate that a large vaccination rate or a short pulse of vaccination or a long latent period is a sufficient condition for the extinction of the disease

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

almost periodic solutions for an impulsive delay nicholson s blowflies model by means of the contraction mapping principle and gronwall bellman s inequality we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay nicholson s blowflies model the main results are illustrated by an example

stochastic nicholson type delay differential system focusing on nicholson type delay differential system in random environments we introduce the stochastic system to model the dynamics of nicholson s blowflies population sizes with mortality rates

on existence of a globally attractive periodic solution of impulsive delay logarithmic population model in this paper it is shown that a logarithmic population model which is governed by impulsive delay differential equation has a globally attractive periodic solution

global existence of solutions for semilinear damped wave equations in rn with noncompactly supported initial data abstract we consider the n dimensional cauchy problem in r n for a semilinear damped wave equation with a power type nonlinearity u p for a noncompactly supported initial data which has a small energy we shall derive a global in time existence result in the case when the power of the nonlinear term satisfies 1 2 n p n n 2 this generalizes a previous result due to todorova yordanov j differential equations 174 2001 464 489 which dealt with a solution in the framework of compactly supported initial data

existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model abstract by means of the cauchy matrix we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population

on oscillation of a food limited population model with impulse and delay in this paper we consider a food limited population model with impulsive effect several explicit sufficient conditions are established for oscillation and nonoscillation of solutions of the equations

existence and uniqueness of positive periodic solutions for a neutral logarithmic population model in this paper by using an abstract continuous theorem of k set contractive operator the criteria is established for the existence global attractivity of positive periodic solution of a neutral delay logarithmic population model with multiple delays the result improve the known ones in s p lu w g ge existence of positive periodic solutions for neutral logarithmic population model with multiple delays j comput appl math 166 2 2004 371 383

a comparative study of deterministic and stochastic dynamics for a non autonomous allelopathic phytoplankton model abstract in this paper we investigate a non autonomous competitive phytoplankton model with periodic coefficients in deterministic and stochastic environment respectively we prove the existence of at least one positive periodic solution together with it s global asymptotic stability the existence of periodic solution has been obtained by using the continuation theorem of coincidence degree theory proposed by gaines and mawhin we formulate the corresponding stochastic model by perturbing the growth rate parameters by white noise terms we prove that all the higher order moments of the solution to the stochastic system is uniformly bounded which ensure that the solution of the stochastic system is stochastically bounded we provide easily verifiable sufficient conditions for non persistence in mean extinction and stochastic permanence of the stochastic system sufficient condition for permanence shows that if the noise intensity is very low then the solution of the stochastic system persists in the periodic coexistence domain of the deterministic system we perform exhaustive numerical simulations to validate our analytical findings