Typical Measures on Discrete Time Prey-Predator Model with HarvestedPrey

Abstract

Prey-predator model has received much attention during the last few decades due to its wide range of applications. There are many different kinds of prey-predator models in mathematical ecology. The discrete time models governed by difference equations are more appropriate than the continuous time models to describe the prey-predator relations. Thispaper aims to study the effect of harvested prey species on a Holling type IV prey predator model involving intra-specific competition. Harvesting has a strong impact on the dynamic evolution of a population. This model represents mathematically by nonlinear differential equations. The locally asymptotic stability conditions of all possible equilibrium points were obtained. The stability/instability of nonnegative equilibrium and associated bifurcation were investigated by analysing the characteristic equations. Moreover, bifurcation diagram were obtained for different values of parameters of proposed model. Finally, numerical simulation was used to study the global and rich dynamics of that model.