title: Abundance of stable periodic behavior in a Red Grouse population model with delay: a consequence of homoclinicity.
abstract: 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.
authors.affiliation: Institute of Neuroinformatics, University of Zurich and Swiss Federal Institute of Technology Zurich, Irchel Campus, 8057 Zurich, Switzerland. j.slipantschuk@qmul.ac.uk
authors.forename: Julia
authors.initials: J
authors.lastname: Slipantschuk
authors.forename: Ekkehard
authors.initials: E
authors.lastname: Ullner
authors.forename: Murilo da Silva
authors.initials: Mda S
authors.lastname: Baptista
authors.forename: Mohammed
authors.initials: M
authors.lastname: Zeineddine
authors.forename: Marco
authors.initials: M
authors.lastname: Thiel
mesh_terms: D000818:Animals; D008954:Models, Biological; D017711:Nonlinear Dynamics; D010507:Periodicity; D011157:Population Dynamics