BOGDANOV-TAKENS BIFURCATION OF CODIMENSION 3 IN A PREDATOR-PREY MODEL WITH CONSTANT-YIELD PREDATOR HARVESTING

被引：33
|
作者：
Huang, Jicai [1 ]
Liu, Sanhong [2 ]
Ruan, Shigui [3 ]
Zhang, Xinan [1 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hunan, Peoples R China
[2] Hubei Univ Sci & Technol, Sch Math & Stat, Xianning 437100, Hunan, Peoples R China
[3] Univ Miami, Dept Math, Coral Gables, FL 33146 USA
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2016年 / 15卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Predator-prey model; constant-yield harvesting; Bogdanov-Takens bifurcation of codimension 3; Hopf bifurcaton; homoclinic bifurcation; STABILITY REGIONS; SYSTEMS; DYNAMICS;
D O I：
10.3934/cpaa.2016.15.1041
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, we (J. Huang, Y. Gong and S. Ruan, Discrete Contin. Dynam. Syst. B 18 (2013), 2101-2121) showed that a Leslie-Gower type predator-prey model with constant-yield predator harvesting has a Bogdanov-Takens singularity (cusp) of codimension 3 for some parameter values. In this paper, we prove analytically that the model undergoes Bogdanov-Takens bifurcation (cusp case) of codimension 3. To confirm the theoretical analysis and results, we also perform numerical simulations for various bifurcation scenarios, including the existence of two limit cycles, the coexistence of a stable homoclinic loop and an unstable limit cycle, supercritical and subcritical Hopf bifurcations, and homoclinic bifurcation of codimension 1.
引用
收藏
页码：1041 / 1055
页数：15
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