Coexisting patterns of population oscillations: the degenerate Neimark Sacker bifurcation as a generic mechanism

Details Coexisting patterns of population oscillations: the degenerate Neimark Sacker bifurcation as a generic mechanism Coexisting patterns of population oscillations: the degenerate Neimark Sacker bifurcation as a generic mechanism

2010-07-28

arxiv.org/abs/1007.4981v1

Nonlinear Sciences

Chaotic Dynamics

8 pages, 3 figures

Scientific paper

We investigate a population dynamics model that exhibits a Neimark Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period becomes soon locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation of the second attractor reveal that the bifurcations producing the second attractor occur naturally in this type of system.

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