Multiparametric bifurcation analysis of a basic two stage population model

Baer, S. M., Kooi, B. W., Kuznetzov, Yu. A. and Thieme, H. R. 2006. Multiparametric bifurcation analysis of a basic two stage population model. SIAM Applied Mathematics : subm. 2005/03/01


In this paper we investigate long-term dynamics of the most basic model for stagestructured populations, in which the per capita transition from the juvenile into the adult class is density dependent. The model is represented by an autonomous system of two nonlinear differential equations for a single population. We nd that the interaction of intra-adult competition and intrajuvenile competition gives rise to multiple attractors, one of which can be oscillatory. A detailed numerical study reveals a rich bifurcation structure for this two dimensional system, whose organizing center is a degenerate Bogdanov-Takens (BT) bifurcation point. The corresponding triple critical equilibrium has an elliptic sector, which is demonstrated by the numerical normal form analysis. It is shown that the canonical unfolding of the codim-three BT point reveals the underlying dynamics of the model. Certain new features of this unfolding, which are important in applications but have been overlooked in available theoretical studies, are established. Various three-, two-, and one-parameter bifurcation diagrams of the model are presented and interpreted in biological terms.

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