Stability Analysis of Three Species Food Chain with Competition

We study a food chain system that consists of 1 prey and 2 predators populations. The prey population grows logistically while the predators apply different Holling functional responses. The first predator preys on the prey following Holling type II functional response and the second predator preys on both the prey and the first predator following Holling type II and III functional responses, respectively. 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 are also presented.