The Local Bifurcation of Food Chain Prey-Predator Model with Crowley-Martin-Type of Functional Response

Abstract

In this work, the conditions of the occurrence of the local bifurcation (such as saddle-node, trans critical ,and pitchfork) of all steady points of a food chain model. With fear and Growly-Martin functional response have been established. It is observed that there is a trans critical and pitchfork bifurcations near each of , where as a saddle-node bifurcation near the positive equilibrium point have been occurred. Finally, numerical simulation was used to illustrate the occurrence of the bifurcation of the proposed model.

Keywords

• Prey-predator
• Sotomayor's theorem
• Local bifurcation
• Global bifurcation