title: Basins of attraction for species extinction and coexistence in spatial rock-paper-scissors games.
abstract: We study the collective dynamics of mobile species under cyclic competition by breaking the symmetry in the initial populations and examining the basins of the two distinct asymptotic states: extinction and coexistence, the latter maintaining biodiversity. We find a rich dependence of dynamical properties on initial conditions. In particular, for high mobility, only extinction basins exist and they are spirally entangled, but a basin of coexistence emerges when the mobility parameter is decreased through a critical value, whose area increases monotonically as the parameter is further decreased. The structure of extinction basins for high mobility can be predicted by a mean-field theory. These results provide a more comprehensive picture for the fundamental issue of species coexistence than previously achieved.
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Hongjing
authors.initials: H
authors.lastname: Shi
authors.forename: Wen-Xu
authors.initials: WX
authors.lastname: Wang
authors.forename: Rui
authors.initials: R
authors.lastname: Yang
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
mesh_terms: D003198:Computer Simulation; D003299:Cooperative Behavior; D053476:Extinction, Biological; D005716:Game Theory; D008954:Models, Biological; D011157:Population Dynamics