Stability Analysis and Numerical Simulation of 1 Prey – 2 Predator System

摘要

In this paper, we study an ecological system that consists of 1 prey and 2 predators populations. The prey population grows logistically while Holling type II functional response is applied for both predators . The first predator preys on the prey and the second predator preys on the first one. The study starts with the stability analysis of critical points of the systems. Then, by using normal form and centre manifold method the information about other nontrivial solutions due to bifurcation including possible limit cycles appearance is obtained. The results are confirmed by numerical simulation using MatCont and biological interpretation of the results is also presented.