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<p>This study explores a fractional predator–prey system employing the Caputo fractional derivative to account for memory effects inherent in biological systems. Notably, we extend the traditional fear effect model to include carry-over effects, reflecting the influence of past experiences on current prey behavior. Moreover, we consider the prey’s growth to be subject to the double Allee effect. The stability and bifurcation analysis of the proposed model is made. Our findings indicate that the fractional order significantly impacts the system’s stability, providing insights into the complex interplay between memory and ecological interactions. This research contributes to a deeper comprehension of predator–prey dynamics and offers a novel approach to modeling ecological systems with memory effects. Numerical simulations are provided to illustrate the theoretical results and their biological implications.</p>

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Fear of Predation and its Carry-Over Effect in a Fractional Order Prey-Predator Model with Double Allee Effect

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Hatice Çizmeci,
  • Ercan Balci

摘要

This study explores a fractional predator–prey system employing the Caputo fractional derivative to account for memory effects inherent in biological systems. Notably, we extend the traditional fear effect model to include carry-over effects, reflecting the influence of past experiences on current prey behavior. Moreover, we consider the prey’s growth to be subject to the double Allee effect. The stability and bifurcation analysis of the proposed model is made. Our findings indicate that the fractional order significantly impacts the system’s stability, providing insights into the complex interplay between memory and ecological interactions. This research contributes to a deeper comprehension of predator–prey dynamics and offers a novel approach to modeling ecological systems with memory effects. Numerical simulations are provided to illustrate the theoretical results and their biological implications.