Impact of Cooperative Hunting and Fear-Induced in a Prey-Predator System with Crowley-Martin Functional Response

Abstract

Cooperative hunting among predators and the fear-induced growth rate reduction in prey populations is an ecologically significant phenomenon. Many researchers have studied the effects of hunting cooperation and fear independently, but there has not been much research on the combined effect. This study analyzed a classical predator-prey system incorporating hunting cooperation and fear effect with Crowley-Martin functional response. We have done the basic analysis, including positivity, boundedness of solutions, existence and stability analysis of equilibria, Hopf-bifurcation, saddle-node bifurcation. We analyzed that incorporating cooperative hunting among predators may destabilize the system dynamics by producing limit cycles via Hopf-bifurcation. Furthermore, we noticed that the system shows bi-stability behavior between predator-free equilibrium and the coexistence equilibrium. Also, analysis shows that the system becomes unstable for a fixed hunting cooperation parameter on increasing the strength of fear. To validate the analytical conclusions, numerical simulations are conducted.