Abundance of stable periodic behavior in a Red Grouse population model with delay: A consequence of homoclinicity

Julia Slipantschuk (Corresponding Author), Ekkehard Ullner, Murilo Da Silva Baptista, Mohammed Zeineddine, Marco Thiel

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Shrimp-shaped periodic regions embedded in chaotic regions in two-dimensional parameter spaces are of specific interest for physical and biological systems. We provide the first observation of these shrimp-shaped stability regions in a parameter space of a continuous time-delayed population model, obtained by taking the delays as bifurcation parameters. The parameter space organization is governed by the presence of infinitely many periodicity hubs, which trigger the spiraling organization of these shrimp-shaped periodic regions around them. We provide evidence that this spiraling organization in the parameter space is a consequence of the existence of homoclinic orbits in the phase space.
Original languageEnglish
Article number045117
Number of pages7
Issue number4
Early online date12 Dec 2010
Publication statusPublished - Dec 2010



  • chaotic attractors

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