Degenerate Transcritical Bifurcation Point can be an Attractor: A Case Study in a Slow–Fast Modified Leslie–Gower Model

• Liyan Zhong ^[1] ; Jianhe Shen ^[2]
  1. [1] Fujian Normal University

     Fujian Normal University

     China

     
  2. [2] FJKLMAA and Center for Applied Mathematics of Fujian Province (FJNU)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In general, bifurcation delay occurs near a transcritical bifurcation point of the critical curve in two-dimensional singular perturbation systems. However, if the transcritical bifurcation point is exactly an equilibrium of the model under certain parameter values, what happens near such “degenerate transcritical bifurcation point”? In this paper, by combining geometric singular perturbation theory, center manifold reduction and blow-up technique we show that a degenerate transcritical bifurcation point can be a global attractor via a concrete example—a slow-fast modified Leslie-Gower model.

    That is, bifurcation delay cannot occur near degenerate transcritical bifurcation point in this model. Numerical simulations verify the theoretical predictions.

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