Bogdanov-takens bifurcation of codimension 3 in a predator-prey model with constant-yield predator harvesting

Jicai Huang, Sanhong Liu, Shigui Ruan, Xinan Zhang

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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 bi-furcation (cusp case) of codimension 3. To confirm the theoretical analysis and results, we also perform numerical simulations for various bifurcation sce-narios, 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.

Original languageEnglish (US)
Pages (from-to)1053-1067
Number of pages15
JournalCommunications on Pure and Applied Analysis
Volume15
Issue number3
DOIs
StatePublished - May 1 2016

Fingerprint

Bogdanov-Takens Bifurcation
Predator-prey Model
Harvesting
Predator
Codimension
Cusp
Limit Cycle
Hopf bifurcation
Bifurcation (mathematics)
Homoclinic Loop
Homoclinic Bifurcation
Coexistence
Hopf Bifurcation
Theoretical Analysis
Computer simulation
Bifurcation
Unstable
Singularity
Numerical Simulation
Model

Keywords

  • Bogdanov-Takens bi-furcation of codimension 3
  • Constant-yield harvesting
  • Homoclinic bifurcation
  • Hopf bifurcaton
  • Predator-prey model

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Bogdanov-takens bifurcation of codimension 3 in a predator-prey model with constant-yield predator harvesting. / Huang, Jicai; Liu, Sanhong; Ruan, Shigui; Zhang, Xinan.

In: Communications on Pure and Applied Analysis, Vol. 15, No. 3, 01.05.2016, p. 1053-1067.

Research output: Contribution to journalArticle

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