The Effect of Age Structure and Two Delays on the Predator-prey Model with Prey Fear Cost and Variable Predator Search Speed

Abstract

The predator fertility function $\mathcal{M}(a)$ is thought to be a piecewise function related to the predator development time $\tau_{2}$, and a predator-prey model with predator-age structure and prey reaction time delay $\tau_{1}$ is investigated. By calculating the stability switching curves and using the theory of integrated semigroups and the Hopf bifurcation theory for abstract Cauchy problems with non-dense domain, we obtain that oscillations are caused by $\tau_{1}$ and $\tau_{2}$. Numerical simulations and a summary are presented at the end.