Hopf bifurcation and dynamical behavior of a stage-structured predator sharing a prey

Abstract

In this paper, we divide the predator's life cycle into two stages of foliage maturity, namely immature and mature. Both types of predators have hunting ability and compete for the same prey. Naturally, their consumption rates and growth rates are limited by the presence of the prey population. Therefore, a stage-structured model with Holling type II response function is proposed. The objective of this paper is to investigate the existence of a local Hopf bifurcation. Bifurcation diagrams of one-parameter family and two- parameter family are also expressed into several regions of different dynamical behaviors. Finally, numerical simulations are carried out in support of the theoretical results.