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<p>In this paper, a slow-fast system with piecewise-smooth functional response is established, which is based on a modified Leslie-Gower model incorporating Michaelis-Menten type nonlinear harvesting. The existence conditions for a unique positive interior equilibrium are discussed and the positive invariant region is partitioned based on the equilibrium points. By adjusting the parameters within these divided regions, the system exhibits some dynamics such as singular Hopf bifurcation, canard explosion, relaxation oscillation, the boundary equilibrium bifurcation. And these dynamic phenomena are analyzed, with a focus on a proof of the non-smooth Hopf bifurcation.</p>

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Dynamic Analysis of a Piecewise-Smooth Slow-Fast Leslie-Gower Model with Nonlinear Harvesting

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • Yang Xu,
  • Yue Zhang

摘要

In this paper, a slow-fast system with piecewise-smooth functional response is established, which is based on a modified Leslie-Gower model incorporating Michaelis-Menten type nonlinear harvesting. The existence conditions for a unique positive interior equilibrium are discussed and the positive invariant region is partitioned based on the equilibrium points. By adjusting the parameters within these divided regions, the system exhibits some dynamics such as singular Hopf bifurcation, canard explosion, relaxation oscillation, the boundary equilibrium bifurcation. And these dynamic phenomena are analyzed, with a focus on a proof of the non-smooth Hopf bifurcation.