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Bifurcation analysis in an age-structured model of a single species living in two identical patches. (English) Zbl 1185.34101
Summary: We consider the age-structured model of a single species living in two identical patches derived in So et al. [J. W.-H. So, J. Wu and 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:
34K18Bifurcation theory of functional differential equations
37N25Dynamical systems in biology
92D25Population dynamics (general)
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