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

TL;DR

This paper investigates a predator-prey model with age structure and Michaelis-Menten ratio dependence, analyzing its stability and bifurcation behavior using advanced mathematical theories, and supporting findings with simulations.

Contribution

It introduces a novel analysis of Hopf bifurcation in an age-structured predator-prey model with ratio-dependent response, using integrated semigroup and bifurcation theories.

Findings

Existence of Hopf bifurcation with respect to maturation period

Conditions for stability and oscillations identified

Simulations confirm theoretical predictions

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.