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Liu, Zhihua; Tang, Hui; Magal, Pierre

Hopf bifurcation for a spatially and age structured population dynamics model. (English) Zbl 1348.37112

Discrete Contin. Dyn. Syst., Ser. B 20, No. 6, 1735-1757 (2015).
This paper studies a spatially and age-structured population dynamics model which describes the growth of trees, subject to a Ricker-type birth limitation. This model is restated as an abstract nonlocal problem on \(Y\times L^1((0,\infty),Y)\), where \(Y=L^1((0,1),\mathbb{R})\), and subsequently studied using a Hopf bifurcation theorem for abstract non-densely defined Cauchy problems obtained in [Z. Liu et al., Z. Angew. Math. Phys. 62, No. 2, 191–222 (2011; Zbl 1242.34112)].
The existence of Hopf bifurcations, which occur at a positive age-dependent steady state of the model, is obtained via an analysis of the spectrum of the non-densely defined linear part. This analysis is significantly more complicated than its counterpart for the corresponding model without spatial structure, yielding a first example for the occurrence of a Hopf bifurcation for a spatially and age-structured population dynamics model. The predicted Hopf bifurcations are then illustrated via numerical simulations.
Reviewer: Paul Georgescu (Iaşi)

Cited in 12 Documents

MSC:

37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
35B32 Bifurcations in context of PDEs
92D25 Population dynamics (general)

Keywords:

Hopf bifurcations; population dynamics; age structure; spatial structure; integrated semigroups

Citations:

Zbl 1242.34112
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Full Text: DOI

References:

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