Impact of Fear in a Predator-Prey Model with Crowley-Martin Response for Predation

Predation process play the key role in the dynamics of predator-prey model. Fear in prey populations on account of predator's hunting is an important fact in predation process. The aim of this article is to find out the impact of fear among prey populations on the system behavior in a prey dependent predator-prey model of interacting populations. In this model we considered Crowley -Martin response function for predation and intra-specific competition among predator populations. We offer a detailed mathematical analysis of the proposed model to illustrate some of the significant results that has arisen from the interplay of deterministic ecological phenomena and processes. In particular, stability (local and global) and bifurcation (Hopf-Andronov) analysis of this model are conducted for biologically feasible parameters. We attained sufficient conditions to ensure the global stability of the unique positive equilibrium, by using appropriate Lyapunov functions and Lasalle invariance principle. Finally, numerical simulations through computer illustrate the dynamics of the ecological system