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

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

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 225, issue C, 968-991

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.

Keywords: Mathematical model; Generalist predator; Fear of predator; Prey refuge; Bifurcation; Stochasticity (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:225:y:2024:i:c:p:968-991

DOI: 10.1016/j.matcom.2023.09.022

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