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Stability and bifurcation in an age-structured model with stocking rate and time delays. (English) Zbl 1416.35039

Summary: In this paper, a predator-prey model with age structure, stocking rate and two delays is investigated. We show that Hopf bifurcation occurs when one of the time delay \(\tau\) crosses a sequence of critical values, by applying Hopf bifurcation theory for abstract Cauchy problems with non-dense domain. Numerical simulations are included to verify our results and a summary is also given.

MSC:

35B32 Bifurcations in context of PDEs
92D30 Epidemiology
35L60 First-order nonlinear hyperbolic equations
35L50 Initial-boundary value problems for first-order hyperbolic systems
47D06 One-parameter semigroups and linear evolution equations
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