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.     

Positive almost periodic solution for a class of Nicholson’s blowflies model with a linear harvesting term

In this paper, we study the problem of positive almost periodic solutions for the generalized Nicholson’s blowflies model with a linear harvesting term and multiple time-varying delays. By applying the fixed point theorem and the Lyapunov functional method, we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results.     

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.     

Positive almost periodic solution for a class of Lasota-Wazewska model with infinite delays

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.     

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.     

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.     

ALMOST PERIODIC SOLUTIONS OF SINGLE POPULATION MODELS WITH ALMOST PERIODIC ENVIRONMENT

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＳＩＮＧＬＥＰＯＰＵＬＡＴＩＯＮＭＯＤＥＬＳＷＩＴＨＡＬＭＯＳＴＰＥＲＩＯＤＩＣＥＮＶＩＲＯＮＭＥＮＴＨｅＣｈｏｎｇｙｏｕ（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｔｙ）（何崇佑）南京大学，邮编：２１０００８Ａｂ...     

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.     

DYNAMICS OF THE NONAUTONOMOUS SCHONER MODEL WITH FEEDBACK CONTROL AND DIFFUSION

This paper consider a nonautonomous schoner model with feedback control and diffusion. It is shown that the system can be made persistence. Then the existence and the uniqueness of the positive solutions and positive almost periodic solutions for corresponding periodic system and almost periodic system are also discussed.     

Exponential stability of pseudo almost periodic delayed Nicholson‐type system with patch structure

In this paper, we consider the existence and global exponential stability of positive pseudo almost periodic solutions for a delayed Nicholson‐type system with patch structure. With the aid of ergodic theory and differential inequality technique, we prove the existence and global exponential stability of positive pseudo almost periodic solutions for the addressed system, which generalize and improve some known results. Specially, an example and its numerical simulations are provided to manifest the effectiveness of theoretical results.     

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.     

Multiple positive almost periodic solutions to an impulsive non-autonomous Lotka–Volterra predator–prey system with harvesting terms

In this paper, by using Mawhin’s continuation theorem of coincidence degree theory, we study an impulsive non-autonomous Lotka–Volterra predator–prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive almost periodic solutions for the system under consideration. Our results of this paper are completely new and our method used in this paper can be used to study the existence of multiple positive almost periodic solutions to other types of population systems.     

Pseudo almost periodic solutions for a model of hematopoiesis with a feedback control

In this paper, a generalized model of hematopoiesis is considered with the introduction of a feedback control and continuously distributed delays. By using Lyapunov functional method and differential inequality techniques, we obtain some sufficient conditions for the existence and global exponential stability of positive pseudo almost periodic solutions of this model. We also provide numerical simulations to support the theoretical results.     

一类带反馈控制的非自治离散竞争系统概周期解的动力学性质

本文利用差分方程的比较原理以及构造国合适的Lyapunov函数,讨论了一类带有反馈控制的非自治离散竞争系统的持久性和概周期解,给出了存在正概周期解的几个充分条件.最后给出一个数值例子验证了本文主要结果的有效性.     

具有阶段结构且食饵有避难所的模型分析

研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

一类非线性延迟积分方程正的概周期型解的存在性

本文利用不动点理论,给出了一类非线性延迟积分方程正的概周期型解的存 在性条件.     

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.     

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.     

Periodic solutions of a nonautonomous periodic model of population with continuous and discrete time

In this paper, we employ the Mawhin's continuation theorem to study the existence of positive periodic solutions of the nonautonomous periodic model of population with continuous and discrete time. It is interesting that the conditions to guarantee the existence of positive periodic solutions of discrete time model are similar to those for the corresponding continuous time model.     

Four positive periodic solutions for the first order differential system

In this paper, we establish the existence of four positive periodic solutions for the first order differential system by using the continuation theorem of coincidence degree theory. When our result is applied to a competition Lotka-Volterra population model, we obtain the existence of four positive periodic solutions for this model.