Relaxation Oscillation, Homoclinic Orbit and Limit Cycles in a Piecewise Smooth Predator–Prey Model

• Jinhui Yao ^[1] ; Jicai Huang ^[1] ; Hao Wang ^[2]
  1. [1] Central China Normal University

     Central China Normal University

     China

     
  2. [2] University of Alberta

     University of Alberta

     Canadá

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01154-1
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we revisit a piecewise smooth fast-slow predator–prey model with Holling type I functional response and predator harvesting, where the harvesting rate is sufficiently small compared to the intrinsic growth rate of prey. The model undergoes two bifurcation mechanisms: (i) singular slow-fast cycle bifurcation, through which the model can have a unique and stable relaxation oscillation or homoclinic orbit; (ii) boundary equilibrium bifurcation, from which a unique and unstable limit cycle occurs. Additionally, we show the coexistence of a large-amplitude relaxation oscillation (or homoclinic orbit) and a small-amplitude limit cycle.

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