<p>Intraspecific predation, commonly known as cannibalism, is a naturally occurring phenomenon that significantly influences the structure and function of ecological systems. This study investigates the stability and bifurcation dynamics of a cannibalistic predator-prey model incorporating fear effects and prey refuge. We rigorously analyze the existence and stability conditions of the equilibrium points, demonstrating that the system exhibits complex behaviors, including period-doubling and Neimark-Sacker bifurcations. The influence of key parameters—particularly the fear effect (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1370_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$\phi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>) and step size (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1370_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>) –is examined as bifurcation parameters to assess their role in species coexistence and ecological balance. Numerical simulations validate theoretical results through phase portraits, bifurcation diagrams, Lyapunov exponent analysis, and local stability assessments. To mitigate chaotic dynamics, we implement Ott-Grebogi-Yorke (OGY) control, demonstrating its efficacy in stabilizing the system. By extending the analysis to a networked framework, we explore how coupling strength and network topology influence the dynamical behavior of interconnected predator–prey populations. Our findings provide critical insights into predator-prey interactions under behavioral adaptations, offering valuable implications for ecological conservation and sustainable species management. Varying fear intensity and refuge proportion results in noticeable transitions in population behavior, as evident in the bifurcation diagrams.</p>

Ecological Dynamics of a Predator-Prey Model with Cannibalism, Refuge, and Fear: A Bifurcation and Chaos Control Perspective

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发表日期：

2025年9月10日

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Md. Jasim Uddin,
Md. Mutakabbir Khan,
Ibraheem M. Alsulami,
Nehad Ali Shah

摘要

Intraspecific predation, commonly known as cannibalism, is a naturally occurring phenomenon that significantly influences the structure and function of ecological systems. This study investigates the stability and bifurcation dynamics of a cannibalistic predator-prey model incorporating fear effects and prey refuge. We rigorously analyze the existence and stability conditions of the equilibrium points, demonstrating that the system exhibits complex behaviors, including period-doubling and Neimark-Sacker bifurcations. The influence of key parameters—particularly the fear effect ( $\phi $ $ϕ$ ) and step size ( $\mu $ $μ$ ) –is examined as bifurcation parameters to assess their role in species coexistence and ecological balance. Numerical simulations validate theoretical results through phase portraits, bifurcation diagrams, Lyapunov exponent analysis, and local stability assessments. To mitigate chaotic dynamics, we implement Ott-Grebogi-Yorke (OGY) control, demonstrating its efficacy in stabilizing the system. By extending the analysis to a networked framework, we explore how coupling strength and network topology influence the dynamical behavior of interconnected predator–prey populations. Our findings provide critical insights into predator-prey interactions under behavioral adaptations, offering valuable implications for ecological conservation and sustainable species management. Varying fear intensity and refuge proportion results in noticeable transitions in population behavior, as evident in the bifurcation diagrams.