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<p>To assess the impact of time delay, which describes the age-selective harvesting predator, on the dynamics of breeding management models, we propose a switched predator–prey breeding management model with impulsive nonlinear releasing and age-selective harvesting predator. By theories of impulsive differential equations and their relatively mathematically analytical approaches, the globally attractive condition for the prey-free boundary periodic solution of model (<InternalRef RefID="Equ1">2.1</InternalRef>) is presented, the permanent condition for model (<InternalRef RefID="Equ1">2.1</InternalRef>) is also presented. Finally, numerical analysis is inserted to illustrate the results. Bifurcation analysis diagrams for parameters <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2025_3960_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>μ</mi> <mo movablelimits="false">max</mo> </msub> </math></EquationSource> <EquationSource Format="TEX">$\mu _{\max}$</EquationSource> </InlineEquation>, <i>τ</i> and their changes of chaotic solutions are found. Furthermore, parameter <i>θ</i> correlating with time delay also plays an important role in the dynamical behaviors of model (<InternalRef RefID="Equ1">2.1</InternalRef>). Our results provide mathematical theories for more reasonable breeding management.</p>

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Dynamics of a switched predator–prey breeding management model with impulsive nonlinear releasing and age-selective harvesting predator

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月28日

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  • Jianjun Jiao,
  • Yunpeng Xiao,
  • Hui Jiao

摘要

To assess the impact of time delay, which describes the age-selective harvesting predator, on the dynamics of breeding management models, we propose a switched predator–prey breeding management model with impulsive nonlinear releasing and age-selective harvesting predator. By theories of impulsive differential equations and their relatively mathematically analytical approaches, the globally attractive condition for the prey-free boundary periodic solution of model (2.1) is presented, the permanent condition for model (2.1) is also presented. Finally, numerical analysis is inserted to illustrate the results. Bifurcation analysis diagrams for parameters μ max $\mu _{\max}$ , τ and their changes of chaotic solutions are found. Furthermore, parameter θ correlating with time delay also plays an important role in the dynamical behaviors of model (2.1). Our results provide mathematical theories for more reasonable breeding management.