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Stability and Hopf-bifurcation analysis of diffusive Leslie–Gower prey–predator model with the Allee effect and carry-over effects

Author

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  • Ramasamy, Sivasamy
  • Banjerdpongchai, David
  • Park, PooGyeon

Abstract

Identification of the various dynamical kinetics relating to prey–predator interconnection is the main goal of theoretical ecologists. In addition to direct killing (the lethal effect) in prey–predator interactions, a number of studies have suggested that there are some indirect effects (non-lethal), such as fear of predation. This non-lethal effect slows down the growth rate of prey and this phenomenon can be carried over to upcoming seasons or generations. The Allee effect also has an impact not only on prey populations but also on predator populations. Considering these, we first propose a modified Leslie–Gower predator–prey model that takes into account the fear-induced carry-over effect (COE), the predator’s Allee effect, and intraspecific competition among predators. The ecologically viable equilibrium points and corresponding local and global stability criteria are derived for the model. Moreover, we establish the conditions for the occurrence of Hopf-bifurcation around coexistence equilibrium and compute the first Lyapunov coefficient to verify the stability of the limit cycle. Secondly, we extend the proposed model to include the spatial variable by considering the spatial movements of the species. For the spatial model with zero flux boundary conditions, the criteria for Turing instability and Hopf-bifurcation are derived. Numerical simulations aim to verify the theoretical results. Our study suggests that the parameters related to fear-induced COE, the predator’s Allee effect, and intraspecific competition have a greater impact on system dynamics.

Suggested Citation

  • Ramasamy, Sivasamy & Banjerdpongchai, David & Park, PooGyeon, 2025. "Stability and Hopf-bifurcation analysis of diffusive Leslie–Gower prey–predator model with the Allee effect and carry-over effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 19-40.
    • Handle: RePEc:eee:matcom:v:227:y:2025:i:c:p:19-40
    DOI: 10.1016/j.matcom.2024.07.034
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    References listed on IDEAS

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    1. Sharma, Swarnali & Samanta, G.P., 2015. "A Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 69-84.
    2. Fangyuan Hua & Kathryn E. Sieving & Robert J. Fletcher & Chloe A. Wright, 2014. "Increased perception of predation risk to adults and offspring alters avian reproductive strategy and performance," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(3), pages 509-519.
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    4. Feng, Xiaozhou & Liu, Xia & Sun, Cong & Jiang, Yaolin, 2023. "Stability and Hopf bifurcation of a modified Leslie–Gower predator–prey model with Smith growth rate and B–D functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Kumar, Udai & Mandal, Partha Sarathi, 2022. "Role of Allee effect on prey–predator model with component Allee effect for predator reproduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 623-665.
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    9. Pal, Debjit & Kesh, Dipak & Mukherjee, Debasis, 2024. "Cross-diffusion mediated Spatiotemporal patterns in a predator–prey system with hunting cooperation and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 128-147.
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    1. Ramasamy, Sivasamy & Banjerdpongchai, David & Park, PooGyeon, 2026. "Stability and bifurcation analysis of a complex two-prey, one-predator model with carry-over effects, migration, and harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 286-305.

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