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Zbl 1185.34101
Yu, Chunbo; Wei, Junjie; Zou, Xingfu
Bifurcation analysis in an age-structured model of a single species living in two identical patches. (English)
[J] Appl. Math. Modelling 34, No. 4, 1068-1077 (2010). ISSN 0307-904X

Summary: We consider the age-structured model of a single species living in two identical patches derived in So et al. [{\it J. W.-H. So, J. Wu} and {\it X. Zou}, J. Math. Biol. 43, No.1, 37--51 (2001; Zbl 0986.92039)]. We chose a birth function that is frequently used but different from the one used in So et al. which leads to a different structure of the homogeneous equilibria. We investigate the stability of these equilibria and Hopf bifurcations by analyzing the distribution of the roots of associated characteristic equation. By the theory of normal form and center manifold, an explicit algorithm for determining the direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived. Finally, some numerical simulations are carried out for supporting the analytic results.

MSC 2000:: *34K18 Bifurcation theory of functional differential equations
37N25 Dynamical systems in biology
92D25 Population dynamics

Keywords: age-structured model; delay; homogeneous equilibrium; Hopf bifurcation; periodic solutions

Citations: Zbl 0986.92039

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