Criminals Treated as Predators to Be Harvested: A Two Prey One Predator Model with Group Defense, Prey Migration and Switching

Abstract

A mathematical model is formulated and analysed to study the dynamics of a one predator - two prey eco-system using the logistic equation in which the predator switches between habitats and is being harvested. Constant effort and Constant yield harvesting functions are applied to the predators. The Constant effort strategy as opposed constant yield strategy may lead to an additional equilibrium in which the predators are extinct, whereas in the Constant yield stategy the only equilibrium is the coexistence one. In both cases, computer simulations are performed to study the effects of various parameters on the dynamics of the system. These studies show that depending on parameter values, a stable equilibrium or a limit cycle orbit is possible with both harvesing types.