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

被引：15

作者：

Liang, Zhiqing ^{[1
]}

Zeng, Xiaping ^{[1
]}

Pang, Guoping ^{[1
]}

Liang, Yanhong ^{[1
]}

机构：

[1] Yulin Normal Univ, Coll Math & Stat, Guangxi Coll & Univ Key Lab Complex Syst Optimiza, Yulin 537000, Guangxi, Peoples R China

来源：

NONLINEAR DYNAMICS | 2017年 / 89卷 / 04期

关键词：

Leslie predator-prey system; Limit cycle; Successor function; Order-1 periodic solution; State impulsive feedback control; FOOD-CHAIN SYSTEM; QUALITATIVE-ANALYSIS; GLOBAL STABILITY; MULTIPLE DELAYS; MODEL; BIFURCATION; DYNAMICS;

D O I：

10.1007/s11071-017-3637-4

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

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

页码：2941 / 2955

页数：15

共 39 条

[1] The nature of predation: prey dependent, ratio dependent or neither? [J].