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

作者：Huang, Jicai; Liu, Sanhong; Ruan, Shigui^*; Zhang, Xinan

来源：Communications on Pure and Applied Analysis, 2016, 15(3): 1041-1055.

DOI：10.3934/cpaa.2016.15.1041

• Predator-prey model
• constant-yield harvesting
• Bogdanov-Takens bifurcation of codimension 3
• Hopf bifurcaton
• homoclinic bifurcation

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.

• 出版日期2016-5
• 单位湖北科技学院; 华中师范大学