Local Stability Analysis On Lotka-Volterra Predator-Prey Models Functional Responses With Constant prey Refuge

The dynamical behaviours of the predators and prey can be described by studying the local stability of the planar systems. Type I functional response shows that the rate of consumption per predator is proportional to prey’s density while type II functional response is related to the situation that predators would reach satiation as they consumed sufficient amount of prey. We seek out a method of using transformation to reduce the number of parameters of original models and then study the stability analysis of equilibrium points. Under suitable restrictions on the new parameters, we prove that the positive interior equilibrium is a stable node for the system of type I and type II functional responses. Moreover, in the case of type II functional response, the boundary equilibria can have more types of stability other than saddle points.