• DOI:10.1137/050627757
• Corpus ID: 15256852

Multiparametric Bifurcation Analysis of a Basic Two-Stage Population Model

@article{Baer2006MultiparametricBA,
  title={Multiparametric Bifurcation Analysis of a Basic Two-Stage Population Model},
  author={Steven M. Baer and Bob W. Kooi and Yuri A. Kuznetsov and Horst R. Thieme},
  journal={SIAM J. Appl. Math.},
  year={2006},
  volume={66},
  pages={1339-1365}
}

• S. Baer, B. Kooi, +1 author H. Thieme
• Published 31 July 2006
• Mathematics
• SIAM J. Appl. Math.

In this paper we investigate long-term dynamics of the most basic model for stage-structured 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 with four parameters for a single population. We find that the interaction of intra-adult competition and intra-juvenile 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, originating from a degenerate Bogdanov--Takens (BT) bifurcation point when one parameter is kept constant. Depending on the value of this fixed parameter, the corresponding triple critical equilibrium has either an elliptic sector or it is a topological focus, which is demonstrated by the numerical normal form analysis. It is shown that the canonical unfolding of the codimension-three BT point reveals the underlying dynamics of...