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<p>This paper investigates the fast-slow dynamics of Leslie-Gower model with piecewise-smooth response functions and weak Allee effect. Our results indicate that, except the canard explosion phenomenon, the system also exhibits a supercritical superexplosion. Then, due to the existence of piecewise-smooth function and weak Allee effects, the cyclicity of the fast-slow limit periodic set is 3. Finally, we also present the generation mechanism of the double-headed canard cycle. Numerical simulations verify our results.</p>

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Singular Hopf Bifurcation in a Leslie-Gower Fast-Slow Predator-Prey Model with Piecewise Smooth Response

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Kexin Chen,
  • Jun Li,
  • Kaiqi Tang

摘要

This paper investigates the fast-slow dynamics of Leslie-Gower model with piecewise-smooth response functions and weak Allee effect. Our results indicate that, except the canard explosion phenomenon, the system also exhibits a supercritical superexplosion. Then, due to the existence of piecewise-smooth function and weak Allee effects, the cyclicity of the fast-slow limit periodic set is 3. Finally, we also present the generation mechanism of the double-headed canard cycle. Numerical simulations verify our results.