Periodic solution of a Leslie predator–prey system with ratio-dependent and state impulsive feedback control

被引：5
|
作者：
Zhiqing Liang
Xiaping Zeng
Guoping Pang
Yanhong Liang
机构：
[1] Yulin Normal University,College of Mathematics and statistics, Guangxi Colleges and Universities Key Lab of Complex System Optimization and Large Data Processing
来源：
Nonlinear Dynamics | 2017年 / 89卷
关键词：
Leslie predator–prey system; Limit cycle; Successor function; Order-1 periodic solution; State impulsive feedback control;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a Leslie predator–prey system with ratio-dependent and state impulsive feedback control is investigated by applying the geometry theory of differential equation. When the economic threshold level is under the positive equilibrium, the existence, uniqueness and orbital asymptotical stability of order-1 periodic solution for the system can be obtained. When the economic threshold level is above the positive equilibrium, and the positive equilibrium is a focus point, sufficient conditions of the existence, uniqueness and orbital asymptotical stability of order-1 periodic solution for the system are also acquired. Furthermore, when the positive equilibrium is an unstable focus point, the existence of order-1 periodic solution of the impulsive system can be obtained within limit cycle of the continuous system. The mathematical results can be verified by numerical simulations.
引用
收藏
页码：2941 / 2955
页数：14
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