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A generalist predator–prey system with the effects of fear and refuge in deterministic and stochastic environments

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  • Mondal, Bapin
  • Ghosh, Uttam
  • Sarkar, Susmita
  • Tiwari, Pankaj Kumar

Abstract

In the present study, we investigate the dynamics of a generalist predator–prey system by considering that the fear of predators suppresses the birth rate and enhances the intraspecies competition of the prey species. Also, we assume that a constant proportion of the prey population is taking refuge, which results in a reduction in the predation pressure. We consider Cosner functional response to describe the interactions between prey and predator species. We rigorously analyze the proposed model analytically as well as numerically. We see that the system exhibits multi-stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including saddle–node, Hopf and transcritical bifurcations with varying degrees of fear, on the prey’s reproduction and intraspecies competition, induced by the predator species. The emergence of multistability scenarios in the system is also stimulated by the birth rate of prey species and the growth in predator species due to the additional food sources. We modify our proposed model to its stochastic counterpart by considering the impact of environmental white noises on the natural death rates of both prey and predator species. The simulation results for the stochastic system demonstrate that the fluctuations in the densities of prey and predator populations due to stochastic perturbations are highly sensitive to the intensities of the environmental noises. Additionally, we find that the stochastic system showcases noise-induced transitions whenever the deterministic system exhibits bistability.

Suggested Citation

  • Mondal, Bapin & Ghosh, Uttam & Sarkar, Susmita & Tiwari, Pankaj Kumar, 2024. "A generalist predator–prey system with the effects of fear and refuge in deterministic and stochastic environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 968-991.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:968-991
    DOI: 10.1016/j.matcom.2023.09.022
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    References listed on IDEAS

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    1. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    2. Sk, Nazmul & Tiwari, Pankaj Kumar & Pal, Samares, 2022. "A delay nonautonomous model for the impacts of fear and refuge in a three species food chain model with hunting cooperation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 136-166.
    3. Sudeshna Mondal & G. P. Samanta & Juan J. Nieto & Eberhard O. Voit, 2021. "Dynamics of a Predator-Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect," Complexity, Hindawi, vol. 2021, pages 1-38, July.
    4. Roy, Jyotirmoy & Alam, Shariful, 2020. "Fear factor in a prey–predator system in deterministic and stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
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