Periodic dynamics of a switching model with multiple stable states and linear harvest

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Abstract

Fishing moratoriums are vital for fishery management, restoring fish stocks, safeguarding ecosystems, and ensuring sustainable development. In this study, we explored and studied a canonical model with a Holling type-III functional response consisting of two sub-equations switching each other. If the length of the closed season $\bar{T} \leq T^{*}$, the trivial steady state is globally asymptotically stable. For $\bar{T}>T^{*}$, we provided a complete analysis of the existence of a unique periodic solution and three exact periodic solutions. We also provided sufficient conditions for the existence of a globally asymptotically stable periodic solution. Finally, numerical examples were provided to illustrate the theoretical results.

Keywords

periodic solutions / switching dynamical systems / Holling type-III functional response / global asymptotic stability

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