Tristable Phenomenon in a Predator-Prey System Arising from Multiple Limit Cycles Bifurcation

Jiao Jiang, Wenjing Zhang, Pei Yu

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator-prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems.

Original languageEnglish
Article number2050129
JournalInternational Journal of Bifurcation and Chaos
Volume30
Issue number9
DOIs
StatePublished - Jul 1 2020

Keywords

  • Holling type functional response
  • Hopf bifurcation
  • Predator-prey system
  • bistable, tristable
  • focus value
  • limit cycle
  • normal form

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