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.
|Number of pages||4|
|Journal||Physical Review. E, Statistical, Nonlinear and Soft Matter Physics|
|Publication status||Published - Mar 2010|