Modelling the fear effect in prey predator ecosystem incorporating prey patches

Abstract

In an ecosystem, the balance of prey-predator system is greatly influenced by the availability of prey and the fear imposed on
it’s population. In this paper, it is proposed that a prey-predator model in which prey is assumed to be able to detect the presence of predator and to counteract it by forming patches and incorporating the cost of fear into prey reproduction. Equilibrium points are calculated and analysis of the local and global asymptotic behaviors of the system are done. Hopf-bifurcation is seen in case of adequate availability of prey. The system stabilizes in presence of high levels of fear. Availability of prey act as a crucial role to change the dynamics of the system. Numerical simulations showcases the relationship between prey patches and other related parameters like level of fear, conversion rate of predator and availability of prey. These simulations reveal the impact of fear on the prey-predator system and also justify the theoretical findings. In the end, the bifurcation scenarios are derived when two different parameters switch together at a same time. Numerical simulations are justified the theoretical findings.