title: Coexisting patterns of population oscillations: the degenerate Neimark-Sacker bifurcation as a generic mechanism.
abstract: 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.
authors.affiliation: Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany.
authors.forename: Christian
authors.initials: C
authors.lastname: Guill
authors.forename: Benjamin
authors.initials: B
authors.lastname: Reichardt
authors.forename: Barbara
authors.initials: B
authors.lastname: Drossel
authors.forename: Wolfram
authors.initials: W
authors.lastname: Just
mesh_terms: D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D009991:Oscillometry / Q000379:methods*; D011157:Population Dynamics; D013559:Symbiosis / Q000502:physiology*