Eur. Phys. J. Plus (2022) 137: 70
https://doi.org/10.1140/epjp/s13360-021-02219-9

Regular Article

A comparison study of predator–prey system in deterministic and stochastic environments influenced by fear and its carry-over effects

Department of Mathematics, Indian Institute of Engineering Science and Technology, 711103, Shibpur, Howrah, India

^b g_p_samanta@yahoo.co.uk, gpsamanta@math.iiests.ac.in

Received: 19 September 2021
Accepted: 22 November 2021
Published online: 28 December 2021

Abstract

Allee effects driven by predator can play a significant role in the dynamics of low population which mainly occur when a generalist predator follows Holling type II functional response. However, apart from direct consumption (lethal effect of predation), there are some indirect (nonlethal) effects in the presence of predator such as fear effect. Also, this effect can be carried over to the next generation and from generation to generation. In this work, we analyze the dynamics of a predator–prey interaction with the impact of predator’s (a generalist predator with constant biomass) fear and its carry-over effects. First, we investigate the effect of predator’s fear on a single-species system neglecting the predation term. Next, we study the dynamics of Holling type II predator–prey system with the influence of prey refuge. Basic dynamical properties, as well as global stability of each equilibria, have been studied. It is observed that both the fear and its carry-over effects have great impact on the stability of the interior equilibrium point. Moreover, the phenomenon “paradox of enrichment” is shown in our proposed system and classical Holling type II model but it can be ruled out in the absence of carry-over effect. Further, we notice that prey refuge has great impact on the persistence of the predator population. Lastly, our proposed system has been compared with a stochastic model using Gaussian white noise terms due to the effect of fluctuating environment.