A delay nonautonomous model for the impacts of fear and refuge in a three species food chain model with hunting cooperation

Nazmul Sk, Pankaj Kumar Tiwari and Samares Pal

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 192, issue C, 136-166

Abstract: In this article, we study the dynamics of a three species food chain model for a predator–prey system with hunting cooperation in predators; due to fear of predation risk, prey population shows anti-predator behavior. Fear of middle-predator affects the growth rate of prey and the fear of top-predator reduces the predation of middle-predator on prey species. The prey and middle-predator are assumed to take refuge against predation. Numerical results confirm the stabilizing role of refuge whereas hunting cooperation destroys stability and induces limit cycle oscillations. We find that the fear of middle-predator on prey has tendency to stabilize the system while the fear of top-predator on middle-predator creates instability in the system. Further, time delays are considered in the processes of taking refuges and hunting cooperations. Delay in hunting cooperations creates multiple stability switches in the system. Furthermore, seasonal forcing of parameters related to refuges and hunting cooperations depicts a more realistic scenario. We investigate the behaviors of seasonally forced system in the absence as well as presence of time delays. The seasonally forced system exhibits different types of periodic solutions. Complex bursting patterns are observed due to periodicity in refuge of middle-predator (cooperation of top-predator).

Keywords: Mathematical model; Fear; Refuge; Hunting cooperation; Time delay; Seasonality (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:192:y:2022:i:c:p:136-166

DOI: 10.1016/j.matcom.2021.08.018

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