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

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 soon becomes 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.