Codimension two and three bifurcations of a predator–prey system with group defense and prey refuge

Abstract

A predator–prey system with nonmonotonic functional response and prey refuge is considered. We mainly obtain that the system has the bifurcations of cusp-type codimension two and three, these illustrate that the dynamic behaviors of the model with prey refuge will become more complicated than the system with no refuge.

Keywords

• prey refuge
• saddle-node bifurcation
• Bogdanov–Takens bifurcation