Persistence and Almost Periodic Solutions in a Model of Plankton Allelopathy with Impulsive Effects  

作　　者：Lijun XU Yaqin LI Yonghong YANG Tianwei ZHANG 

机构地区：[1]School of Mathematics and Computer Science, Panzhihua University [2]Department of Mathematics, Kunming University [3]School of Essential Education, Yunnan Minzu University [4]City College, Kunming University of Science and Technology

出　　处：《Journal of Mathematical Research with Applications》2016年第2期201-212,共12页数学研究及应用（英文版）

基　　金：Supported by the Scientific Research Fund of Yunnan Provincial Education Department(Grant No.2014Y388)

摘　　要：This paper is concerned with an almost periodic model of plankton allelopathy with impulsive effects. By using the comparison theorem and the Lyapunov method of the impulsive differential equations, sufficient conditions which guarantee the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution of the model are obtained. The main results in this paper improve the work in recent years. And the method used in this paper provides a new method to study the permanence, uniform asymptotical stability and almost periodic solution of the models with impulsive perturbations in biological populations. An example and numerical simulations are provided to illustrate the main results of this paper. Finally, a conclusion is also given to discuss how the impulsive effects influence the permanence, almost periodic solutions and uniform asymptotical stability of the model.This paper is concerned with an almost periodic model of plankton allelopathy with impulsive effects. By using the comparison theorem and the Lyapunov method of the impulsive differential equations, sufficient conditions which guarantee the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution of the model are obtained. The main results in this paper improve the work in recent years. And the method used in this paper provides a new method to study the permanence, uniform asymptotical stability and almost periodic solution of the models with impulsive perturbations in biological populations. An example and numerical simulations are provided to illustrate the main results of this paper. Finally, a conclusion is also given to discuss how the impulsive effects influence the permanence, almost periodic solutions and uniform asymptotical stability of the model.

关 键 词：almost periodic solution permanence uniformly asymptotically stable impulse plankton allelopathy 

分 类 号：O175[理学—数学]