Stability and Bifurcation in a Predator-Prey Model with Age Structure and Delays

摘要

This paper investigates a predator-prey model with age structure and two delays. By formulating the age-structured model with delays as a non-densely defined Cauchy problem and applying the theory of integrated semigroup and recently established Hopf bifurcation theory for abstract Cauchy problems with non-dense domain, we show that Hopf bifurcation occurs in the model. This also shows the sensitivity of the model dynamics on the threshold which might be taken as a measure of a biological maturation period and a time lag between conception and birth. Numerical simulations are performed to illustrate the obtained results and a summary is given.