Oscillation and attractivity of discrete nonlinear delay population model

In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.     

OSCILLATION AND GLOBAL ATTRACTIVITY OF IMPULSIVE PERIODIC DELAY RESPIRATORY DYNAMICS MODEL

This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique positive periodic solution. Some sufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivity of the periodic solution are obtained.     

Existence and global attractivity of unique positive almost periodic solution for a model of hematopoiesis

Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.     

一类时滞微分系统的周期解

研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.     

Positive periodic solutions for impulsive predator-prey model with dispersion and time delays

In this paper, we study the existence and global attractivity of positive periodic solutions for impulsive predator-prey systems with dispersion and time delays. By using coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions, and by means of a suitable Lyapunov functional, the uniqueness and global attractivity of positive periodic solution is presented. Some known results subject to the underlying systems without impulses are improved and generalized.     

Existence and global attractivity of positive periodic solutions of competition systems

In this paper, we study the existence and global attractivity of periodic solutions of a competition system. We obtain sufficient conditions for the existence and global attractivity of positive periodic solutions by Krasnoselskii’s fixed point theorem and the construction of Lyapunov functions.     

具有遗传效应单种群模型的正周期解

利用重合度理论中的延拓定理和Ｌｙａｐｕｎｏｖ泛函方法,讨论了具有遗传效应单种群模型正周期解的存在性和全局吸引性,得到了一些新结果,推广了某些相关结果。     

Existence and global attractivity of positive periodic solutions for impulsive predator–prey model with dispersion and time delays

In this paper, we study the existence and global attractivity of positive periodic solutions for impulsive predator–prey systems with dispersion and time delays. By using the method of coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solution, and by means of a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Some known results subject to the underlying systems without impulses are improved and generalized.     

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].     

Stability and attractivity of periodic solutions of parabolic systems with time delays

This paper is concerned with the existence, stability, and global attractivity of time-periodic solutions for a class of coupled parabolic equations in a bounded domain. The problem under consideration includes coupled system of parabolic and ordinary differential equations, and time delays may appear in the nonlinear reaction functions. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. The existence of time-periodic solutions is for a class of locally Lipschitz continuous reaction functions without any quasimonotone requirement using Schauder fixed point theorem, while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme. The results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system. Applications are also given to three Lotka-Volterra reaction diffusion model problems, and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions.     

Complex dynamics of a delayed stage-structured predator-prey model with impulsive effect

In this paper, we investigate a stage-structured predator-prey model with periodic harvesting (catching or poisoning) for the prey and stage structure for the predator with constant maturation time delay. Sufficient conditions which guaranteed the global attractivity of predator-extinction periodic solution and permanence of the system are obtained. Furthermore, influences of the impulsive perturbation on the inherent oscillation are studied, which exhibits a wide variety of dynamic behaviors by numerical simulations.     

Existence and Attractivity of <Emphasis Type="Italic">k</Emphasis>-Pseudo Almost Automorphic Sequence Solution of a Model of Bidirectional Neural Networks

In this paper we discuss the existence and global attractivity of k-pseudo almost automorphic sequence solution of a model of bidirectional cellular neural networks. We consider the corresponding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution. The k-pseudo almost automorphic sequence solutions generalize the results of pseudo almost periodic, almost periodic and almost automorphic sequences solutions. Moreover the results proved in this paper are new and compliment the existing one.     

一个造血模型周期解的存在性及其性态

本文得到一个造血模型存在周期解的充分条件，并推出方程全部正解关于这个周期解全局和周期解相交的充分条件。     

Oscillation and Global Attractivity in a Nonlinear Delay Periodic Model of Population Dynamics

In this article we shall consider the following nonlinear delay differential equation $$x'(t) + p(t)x(t)-\frac {q(t)x(t)}{r + x^{n}(t-m\omega )} = 0\eqno (*)$$ where m and n are positive integers, p ( t ) and q ( t ) are positive periodic functions of period y . In the nondelay case we shall show that (*) has a unique positive periodic solution $ \overline {x}(t), $ and provide sufficient conditions for the global attractivity of $ \overline {x}(t) $ . In the delay case we shall present sufficient conditions for the oscillation of all positive solutions of (*) about $ \overline {x}(t), $ and establish sufficient conditions for the global attractivity of $ \overline {x}(t). $     

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.     

ON A PERIODIC VOLTERRA EQUATION WITH SEVERAL FINITE DELAYS AND AN INFINITE DELAY

The existence of positive periodic solutions for a periodic Volterra equation with several finite delays and an infinite delay is established. Sufficient conditions for the periodic solutions having global attractivity are obtained.     

Nonautonomous Lotka-Volterra Systems with Delays

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.     

Asymptotic behavior of solutions of a periodic diffusion system of plankton allelopathy

This paper is concerned with the existence and asymptotic behavior of periodic solutions for a periodic reaction diffusion system of a planktonic competition model under Dirichlet boundary conditions. The approach to the problem is by the method of upper and lower solutions and the bootstrap argument of Ahmad and Lazer. It is shown under certain conditions that this system has positive or semi-positive periodic solutions. A sufficient condition is obtained to ensure the stability and global attractivity of positive periodic solutions.     

捕食者具脉冲扰动与相互干扰的阶段结构时滞捕食-食饵模型

讨论了与害虫管理相关的一类捕食者具脉冲扰动与相互干扰的阶段结构时滞捕食-食饵模型,得到了害虫灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.我们的结论为现实的害虫管理提供了一定的理论依据.     

Global stability of autonomous and nonautonomous hepatitis B virus models in patchy environment

Autonomous and nonautonomous hepatitis B virus infection models in patchy environment are investigated respectively to illustrate the influences of population migration and almost periodicity for infection rate on the spread of hepatitis B virus. The basic reproduction number is determined and asymptotic stabilities of disease-free and endemic equilibria are established in case of autonomous system. Moreover, in the nonautonomous system case, existence and global attractivity of almost periodic solution for this system are studied. Finally, feasibility of main theoretical results is showed with the aid of numerical examples for model with two patches.