Impact of predator fear on two competing prey species

Predator-prey interaction is a fundamental feature in the ecological system. The majority of studies has addressed how competition and predation affect species coexistence. Recent field studies on vertebrate has shown that fear of predators can influence the behavioural pattern of prey populations and reduce their reproduction. A natural question arises whether species coexistence is still possible or not when predator induce fear on competing species. Based on the above observation, we propose a mathematical model of two competing prey-one predator system with the cost of fear that affect reproduction rate of both the prey population. To make the model more realistic, we incorporate intraspecific competition within the predator population. Biological justification of the model is shown through positivity and boundedness of solutions. Existence and stability of different boundary equilibria are discussed. Condition for the existence of coexistence equilibrium point is derived from showing uniform persistence. Local as well as a global stability criterion is developed. Bifurcation analysis is performed by choosing the fear effect as the bifurcation parameter of the model system. The nature of the limit cycle emerging through a Hopf bifurcation is indicated. Chaotic motion is observed when one of two prey has bigger competitive capacities than the other. Numerical experiments are carried out to test the theoretical results obtained for this model.