Dynamics with riddled basins of attraction in models of interacting populations

Recently it has been shown that when there are chaotic attractors whose basins are such that every point in the basin has pieces of another attractorsʹs basin arbitrarily nearby, the basins are said to be riddled. A key requirement for the occurrence of a riddled basin is the loss of transverse stability of an invariant subspace, of dimension less than the full space, containing a chaotic attractor. This type of complex dynamics has been found in simple models of interacting populations for which the invariant subspace is defined by the extinction of one species. The characterizations and implications of these behaviors for population ecology are discussed.