Hutchinson model of Holling type II with delay in prey

Abstract

The problems in daily life can be solved with mathematical models, such as the model of Lotka-Volterra to find out how growth of animals. This model can be modified into the Predator-Prey Model of Hutchinson with delay time and Response Function of Holling type II in which one as active predator and the other as prey, delay time is considered on prey population with assuming that supporting resources of prey are adequate and this type of response function is as interactions between populations of predator and prey. In this paper, linearization and eigenvalues are used to analyze the stability solution of the fixed point so that it can be known the effect of delay time and response function of this type. There are three fixed points are obtained without delay time with two fixed points are stable under certain conditions, but delay time can change the stability of the fixed point.