Asymptotic analysis of an age-structured predator-prey model with ratio-dependent Holling III functional response and delays. (English) Zbl 1505.92174
Summary: This paper studies the dynamical behavior of a radio-dependent predator-prey model with age structure and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the conditions for existence of the positive equilibrium point are derived. Then, through determining the distribution of eigenvalues, the globally asymptotic stability of the boundary equilibrium and the locally asymptotic stability for the positive equilibrium are obtained, respectively. In addition, it is also shown that a non-trivial periodic oscillation phenomenon through Hopf bifurcation appears under some conditions. Finally, some numerical examples are provided to illustrate the obtained results.
MSC:
| 92D25 | Population dynamics (general) |
| 34D20 | Stability of solutions to ordinary differential equations |
Keywords:
age-structured predator-prey model; time delay; \(C_0\)-semigroup; asymptotical stability; Hopf bifurcationReferences:
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