Homoclinic bifurcation of a ratio-dependent predator-prey system with impulsive harvesting

被引：14
|
作者：
Wei, Chunjin [1 ]
Liu, Junnan [1 ]
Chen, Lansun [2 ]
机构：
[1] Jimei Univ, Sci Coll, Xiamen 361021, Fujian, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
来源：
NONLINEAR DYNAMICS | 2017年 / 89卷 / 03期
关键词：
Allee effect; Successor function; Order-1 periodic solution; Order-1 homoclinic cycle; Homoclinic bifurcation; PERIODIC-SOLUTION; QUALITATIVE-ANALYSIS; BIOECONOMIC MODEL; CHEMOSTAT MODEL; DYNAMICS;
D O I：
10.1007/s11071-017-3567-1
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, we investigate a ratio-dependent prey-predator model with state-dependent impulsive harvesting where the prey growth rate is subject to a strong Allee effect. The existence of order-1 homoclinic cycle is obtained, and choosing as a control parameter, the existence, uniqueness and stability of order-1 periodic solution of the system are discussed by means of the geometry theory of semi-continuous dynamic system. We also investigate that system exhibits the phenomenon of homoclinic bifurcation about parameter . Moreover, the numerical simulations are provided to show the main results. The used methods are intuitive to prove the existence of order-1 periodic solution and homoclinic bifurcation.
引用
收藏
页码：2001 / 2012
页数：12
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