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<p>This paper presents a periodic fisheries management model incorporating delayed decision effects to analyze fish population dynamics during seasonal closed (no fishing) and open (fishing) periods. The model combines a modified logistic growth function for population dynamics with a Michaelis-Menten (Holling-II) harvest response function that explicitly accounts for critical delay times in management impacts. Using the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Poincar\acute{e}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mi>o</mi> <mi>i</mi> <mi>n</mi> <mi>c</mi> <mi>a</mi> <mi>r</mi> <mover accent="true"> <mi>e</mi> <mo>´</mo> </mover> </mrow> </math></EquationSource> </InlineEquation> map and the approach of constructing auxiliary functions, we determine the conditions under which one, two, or no periodic solutions exist in the absence of harvesting delay. Furthermore, constructing a particular solution yields sufficient conditions for the global asymptotic stability of a unique periodic solution in the harvesting delay system. Our results suggest that designing an appropriate length for the closed harvesting season and harvest delay can prevent species extinction. We provide numerical simulations to support our theoretical findings and conclude with a brief discussion.</p>

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Time-Delay Dynamics in Fishery Resources under Periodic Harvesting: Stability and Sustainability Analysis

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Qingwen Yu,
  • Dongshu Wang,
  • Longkun Tang

摘要

This paper presents a periodic fisheries management model incorporating delayed decision effects to analyze fish population dynamics during seasonal closed (no fishing) and open (fishing) periods. The model combines a modified logistic growth function for population dynamics with a Michaelis-Menten (Holling-II) harvest response function that explicitly accounts for critical delay times in management impacts. Using the \(Poincar\acute{e}\) P o i n c a r e ´ map and the approach of constructing auxiliary functions, we determine the conditions under which one, two, or no periodic solutions exist in the absence of harvesting delay. Furthermore, constructing a particular solution yields sufficient conditions for the global asymptotic stability of a unique periodic solution in the harvesting delay system. Our results suggest that designing an appropriate length for the closed harvesting season and harvest delay can prevent species extinction. We provide numerical simulations to support our theoretical findings and conclude with a brief discussion.