一类具无穷时滞 Nicholson’s blowflies模型的正概周期解(英文)

通过利用锥上的不动点定理,本文主要研究具无穷时滞Nicholson’s blowflies模型的正概周期解的存在唯一性.从而得到此正概周期解存在唯一性和指数收敛的充分条件.最后给出一个例子说明本文结果的可行性.     

Uniqueness and exponential stability of almost periodic positive solution for Lasota‐Wazewska model with impulse and infinite delay

In this paper, impulsive Lasota‐Wazewska model with infinite delay is studied. By using fixed point theorem of decreasing operator, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence, which converges to the almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by Liapunov functional. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Existence and exponential stability of unique almost periodic solution for Lasota–Wazewska red blood cell model with perturbation on time scales

This paper deals with Lasota–Wazewska red blood cell model with perturbation on time scales. By applying the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence which converges to the almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by means of Gronwall inequality. Copyright © 2017 John Wiley & Sons, Ltd.     

A COMPETITIVE AND PREY-PREDATOR MODEL WITH STAGE-STRUCTURE

The uniform persistence is proved for a non-autonomous competitive and prey-predator model with ratio-dependent functional response and stage-structure. By constructing a Liapunov functional, we establish the conditions of existence and uniqueness for the positive periodic solution, which is globally asymptotically stable. We get a unique almost periodic solution for an almost periodic system as well under corresponding conditions .by means of the Razumikhin function method.     

Existence and exponential convergence of almost periodic positive solution for Nicholson's blowflies discrete model with linear harvesting term

This paper deals with a discrete Nicholson's blowflies model with linear harvesting term. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential convergence of the almost periodic positive solution by Lyapunov functional. Copyright © 2013 John Wiley & Sons, Ltd.     

Almost periodic solution for Nicholson’s blowflies model with patch structure and linear harvesting terms

In this paper, we study the existence and exponential convergence of positive almost periodic solutions for a class of Nicholson’s blowflies model with patch structure and multiple linear harvesting terms. Under appropriate conditions, we establish some criteria to ensure that the solutions of this system converge locally exponentially to a positive almost periodic solution. Moreover, we give some examples and numerical simulations to illustrate our main results.     

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 the existence and stability of a unique almost periodic solution of Schoener’s competition model with pure-delays and impulsive effects

In this paper, we consider an almost periodic Schoener’s competition model with delays and impulsive effects. Sufficient conditions which guarantee the permanence of the model and the existence of a unique uniformly asymptotically stable positive almost periodic solution are obtained. The result of this paper is completely new. An suitable example is employed to illustrate the feasibility of the main results.     

Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems

In this paper, we study the existence and exponential convergence of positive almost periodic solutions for a class of Nicholson-type delay system. Under proper conditions, we establish some criteria to ensure that the solutions of this system converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results.     

Hopfield神经网络概周期解的存在性和全局吸引性

该文研究Ｈｏｐｆｉｅｌｄ神经网络概周期解的存在性和全局吸性,获得了该网络存在唯一概周期解的充分条件和所有解收敛于此概周期解的充分条件。     

The positive almost periodic solution for Nicholson-type delay systems with linear harvesting terms

In this paper, we study the existence and exponential convergence of positive almost periodic solutions for a class of Nicholson-type delay system with linear harvesting terms. Under appropriate conditions, we establish some criteria to ensure that the solutions of this system converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results.     

Dynamic analysis of a non-autonomous ratio-dependent predator-prey model with additional food

In this paper, a non-autonomous ratio-dependent three species predator-prey system with additional food to top predator was proposed. The permanence of the model is obtained. Based on the continuation theorem, the sufficient conditions for the existence of a periodic solution are obtained. By using the method of Lyapunov function, we prove that the system exists a unique positive almost periodic solution under some certain conditions.     

Global attractivity and almost periodic solution of a discrete mutualism model with delays

In this paper, we consider an almost periodic discrete Lotka–Volterra mutualism model with delays. We first obtain the permanence and global attractivity of the system. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution, which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result. Copyright © 2013 John Wiley & Sons, Ltd.     

时标上具Allee效应的动力学方程的概周期解

本文研究了时标上具Allee效应的可再生资源动力学方程的概周期解的存在性与稳定性.利用线性系统指数二分性与压缩映射不动点定理,得到了方程存在唯一概周期解的充分条件.此外,通过构建适当的Laypunov函数,得到了概周期解是全局指数稳定的充分条件.     

PERMANENCE,PERIODIC AND ALMOST PERIODIC SOLUTIONS OF NONAUTONOMOUS STAGE STRUCTURED POPULATION DYNAMICS WITH TIME DELAY AND DIFFUSION

A nonautonomous stage-structured two species model with time delay anddiffusion is considered. It is shown that the system is uniformly persistent undersome conditions. By discussing the independent subsystem, more brief sufficientconditions are drawn for a unique positive periodic solution which is globallyattractive and the existence of the positive almost periodic solution which isuniformly asymptotically stable by the Razumikhin function method.     

EXISTENCE AND ATTRACTIVITY OF ALMOST PERIODIC SOLUTION FOR HOPFIELD NEURAL NETWORKS WITH VARIABLE COEFFICIENTS

This paper is to study the existence and attractivity of almost periodic solution for Hopfield-Type delay cellular neural networks(HDCNNs) with variable coefficientsby combining the theory of the exponential dichotomy and Lyapunov functionals method and combine with some analysis techniques. We obtain some sufficient conditions to ensure the networks to have a unique almost periodic solution, and all other solutions converge to this solution.     

Existence and exponential convergence of the positive almost periodic solution for a model of hematopoiesis

In this work, we study the existence and global exponential convergence of positive almost periodic solutions for the generalized model of hematopoiesis. Under appropriate conditions, we employ a novel proof to establish some criteria for ensuring that all solutions of this model converge exponentially to the positive almost periodic solution.     

GLOBAL ATTRACTIVITY IN AN ALMOST PERIODIC PREDATOR-PREY-MUTUALIST SYSTEM

In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient conditions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.     

Global dynamics of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses

In this paper, we study a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses. We show the existence of a bounded positive invariant and attracting set. The possibility of existence and uniqueness of positive equilibrium are considered. The asymptotic behavior of the positive equilibrium and the existence of Hopf-bifurcation of nonconstant periodic solutions surrounding the interior equilibrium are considered. The existence and non-existence of periodic solutions are established under suitable conditions. The permanence conditions are also established. We obtained sufficient conditions to ensure the global stability of the unique positive equilibrium, by using suitable Lyapunov functions, LaSalle invariance principle and Dulac’s criterion. We obtained also sufficient conditions for the global stability of the prey-extinction equilibrium when the unique positive equilibrium is not feasible. Finally, numerical simulations are presented to illustrate the analytical results.