Persistence and Almost Periodic Solutions in a Model of Plankton Allelopathy with Impulsive Effects
Received:December 03, 2014  Revised:March 04, 2015
Key Word: almost periodic solution   permanence   uniformly asymptotically stable   impulse   plankton allelopathy  
Fund ProjectL:Supported by the Scientific Research Fund of Yunnan Provincial Education Department (Grant No.2014Y388).
Author NameAffiliation
Lijun XU School of Mathematics and Computer Science, Panzhihua University, Sichuan 617000, P. R. China 
Yaqin LI Department of Mathematics, Kunming University, Yunnan 650031, P. R. China 
Yonghong YANG School of Essential Education, Yunnan Minzu University, Yunnan 650031, P. R. China 
Tianwei ZHANG City College, Kunming University of Science and Technology, Yunnan 650051, P. R. China 
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      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.
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