Hopf bifurcation for a class of predator-prey system with small immigration

Abstract

The subject of this paper concerns with the bifurcation of limit cycles for a predator-prey model with small immigration. Since, in general, the biological systems are not isolated, taking into account immigration in the model becomes more realistic. In this context, we deal with a model with a Holling type Ⅰ function response and study, using averaging theory of second order, the Hopf bifurcation that can emerge under small perturbation of the biological parameters.

Keywords

• predator-prey system
• periodic orbit
• limit cycle
• hopf bifurcation
• averaging equation