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<p>Ecological studies often describe predator-prey interactions through the lens of predator-grazing facilitation. Among the key factors influencing ecological dynamics are environmental fluctuations and memory effects. This paper investigates how mate-finding Allee effects impact a Bazykin-type ecosystem, incorporating predator cooperation during hunting, predator harvesting, memory effects, and environmental variability. We begin by establishing the positivity and boundedness of the proposed ordinary differential equation (ODE) model. Then, we identify all biologically feasible equilibria and analyze their local stability and bifurcation behavior in a deterministic setting. The model is subsequently extended to a stochastic framework using stochastic differential equations (SDEs), where we examine the existence and uniqueness of solutions. To explore transitions between stable states, we apply the Stochastic Sensitivity Function (SSF) method. Furthermore, we incorporate memory effects using fractional differential equations (FDEs) and analyze their influence on the system dynamics. Numerical simulations indicate that memory can delay population growth and serve as a mechanism for controlling stochastic transitions. The paper concludes with a summary of key findings.</p>

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Impact of memory in Bazykin’s type prey-predator systems considering mate-finding Allee effects, cooperative hunting, and predator harvesting in both deterministic and stochastic environments

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Biswajit Paul,
  • Soumik Pandey,
  • Uttam Ghosh

摘要

Ecological studies often describe predator-prey interactions through the lens of predator-grazing facilitation. Among the key factors influencing ecological dynamics are environmental fluctuations and memory effects. This paper investigates how mate-finding Allee effects impact a Bazykin-type ecosystem, incorporating predator cooperation during hunting, predator harvesting, memory effects, and environmental variability. We begin by establishing the positivity and boundedness of the proposed ordinary differential equation (ODE) model. Then, we identify all biologically feasible equilibria and analyze their local stability and bifurcation behavior in a deterministic setting. The model is subsequently extended to a stochastic framework using stochastic differential equations (SDEs), where we examine the existence and uniqueness of solutions. To explore transitions between stable states, we apply the Stochastic Sensitivity Function (SSF) method. Furthermore, we incorporate memory effects using fractional differential equations (FDEs) and analyze their influence on the system dynamics. Numerical simulations indicate that memory can delay population growth and serve as a mechanism for controlling stochastic transitions. The paper concludes with a summary of key findings.