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

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). (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

In this study, the dynamics of a three species food chain model with hunting cooperation in predators and anti-predator behavior in prey population are examined. Results show that refuge plays a stabilizing role in the system, while hunting cooperation disrupts stability and leads to oscillations. Fear of middle-predator tends to stabilize the system, while fear of top-predator creates instability. Time delays in processes and seasonal forcing of parameters result in different types of periodic solutions and complex bursting patterns in the system.