Existence of almost periodic solution of a class of retarded impulsive differential equations

2011 ◽  
Author(s):  
Jinbo Geng ◽  
Zhibin Liu ◽  
Chiyu Pan
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solution ◽  
Almost Periodic

Dynamics of an N-Species Gilpin–Ayala Impulsive Competition System

2019 ◽  
Vol 20 (7-8) ◽  
pp. 737-746
Author(s):  
Libo Wang ◽  
Guigui Xu
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solution ◽  
Asymptotical Stability ◽  
Global Asymptotical Stability ◽  
Almost Periodic ◽  
Competition System

AbstractIn this paper, we consider an N-species Gilpin–Ayala impulsive competition system. By using comparison theorem, Lyapunov functional, and almost periodic functional hull theory of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence, global asymptotical stability, and almost periodic solution of the model. Our results extend some previously known results. The method used in this paper provides a possible method to study the permanence, global asymptotical stability, and almost periodic solution of the models with impulsive perturbations in biological populations.

scholarly journals Dynamics of an Almost Periodic Food Chain System with Impulsive Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yaqin Li ◽  
Wenquan Wu ◽  
Tianwei Zhang
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Food Chain ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Chain System ◽  
Positive Almost Periodic Solution ◽  
Impulsive Perturbations

In order to obtain a more accurate description of the ecological system perturbed by human exploitation activities such as planting and harvesting, we need to consider the impulsive differential equations. Therefore, by applying the comparison theorem and the Lyapunov method of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution in a food chain system with almost periodic impulsive perturbations. The method used in this paper provides a possible method to study the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution of the models with impulsive perturbations in biological populations. Finally, an example and numerical simulations are given to illustrate that our results are feasible.

scholarly journals Ergodicity and asymptotically almost periodic solutions of some differential equations

2001 ◽  
Vol 25 (12) ◽  
pp. 787-801 ◽  
Author(s):  
Chuanyi Zhang
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Ergodic Condition ◽  
Asymptotically Almost Periodic

Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped.

scholarly journals Global Exponential Stability of Almost Periodic Solution for Neutral-Type Cohen-Grossberg Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Lijun Xu ◽  
Qi Jiang ◽  
Guodong Gu
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Impulsive Differential Equations ◽  
Cellular Neural Networks ◽  
Almost Periodic Solution ◽  
Distributed Delays ◽  
Almost Periodic

A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.

Sign in / Sign up

Export Citation Format

Share Document