Hopf bifurcation for a predator-prey model with age structure and ratio-dependent response function incorporating a prey refuge. (English) Zbl 1498.35032
Summary: In this paper, a predator-prey model with age structure and ratio-dependent response function incorporating a prey refuge is investigated. The model is formulated as an abstract non-densely defined Cauchy problem and a sufficient condition for the existence of the positive age-related equilibrium is given. Then using the integral semigroup theory and the Hopf bifurcation theory for semilinear equations with non-dense domain, it is shown that Hopf bifurcation occurs at the positive age-related equilibrium. Numerical simulations are performed to validate theoretical results and sensitivity analyses are presented. The results show that the prey refuge has a stabilizing effect, that is, the prey refuge is an important factor to maintain the balance between prey and predator population.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35B10 | Periodic solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35F61 | Initial-boundary value problems for systems of nonlinear first-order PDEs |
| 35L04 | Initial-boundary value problems for first-order hyperbolic equations |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 92D25 | Population dynamics (general) |
Keywords:
predator-prey model; age structure; abstract non-densely defined Cauchy problem; integral semigroup theoryReferences:
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