Hopf bifurcation of the Michaelis-Menten type ratio-dependent predator-prey model with age structure

Abstract

This paper is devoted to the study of a predator-prey model with predator-age structure that involves Michaelis-Menten type ratio-dependent functional response. We study some dynamical properties of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain. The existence of Hopf bifurcation is established by regarding the biological maturation period $\tau$ as the bifurcation parameter. The computer simulations and sensitivity analysis on parameters are also performed to illustrate the conclusions.