GLOBALLY EXPONENTIALLY STABLE PERIODIC SOLUTION IN A GENERAL DELAYED PREDATOR-PREY MODEL UNDER DISCONTINUOUS PREY CONTROL STRATEGY

被引：11
作者：
Li, Wenjie [1 ]
Huang, Lihong [1 ,2 ,3 ]
Ji, Jinchen [4 ]
机构：
[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
[2] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China
[3] Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China
[4] Univ Technol Sydney, Sch Mech & Mechatron Engn, Broadway, NSW 2007, Australia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Delayed predator-prey model; discontinuous control strategy; periodic solution; globally exponentially stable; DYNAMICAL BEHAVIOR; NEURAL-NETWORKS; SYSTEM; CONVERGENCE;
D O I：
10.3934/dcdsb.2020026
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper studies the solution behaviour of a general delayed predator-prey model with discontinuous prey control strategy. The positiveness and boundeness of the solution of the system is firstly investigated using the comparison theorem. Then the sufficient conditions are derived for the existence of positive periodic solutions using the differential inclusion theory and the topological degree theory. Furthermore, the positive periodic solution is proved to be globally exponentially stable by employing the generalized Lyapunov approach. The global finite-time convergence is also discussed for the system state. Finally, the numerical simulations of four examples are given to validate the correctness of the theoretical results.
引用
收藏
页码：2639 / 2664
页数：26
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