SCALING LAWS FOR NOISE-INDUCED TEMPORAL RIDDLING IN CHAOTIC SYSTEMS

Recent work has considered the situation of riddling where, when a cha otic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to th e basin of another attractor. The existence of invariant subspace ofte n relies on certain symmetry of the system, which is, however, a nonge neric property as system defects and small random noise can destroy th e symmetry. This paper addresses the influence of noise on riddling. W e show that riddling can actually be induced by arbitrarily small nois e even in parameter regimes where one expects no riddling in the absen ce of noise. Specifically, we argue that when there are attractors loc ated off the invariant subspace, the basins of these attractors can be temporally riddled even when the chaotic attractor in the invariant s ubspace is transversely unstable. We investigate universal scaling law s for noise-induced temporal riddling. Our results imply that the phen omenon of riddling is robust, and it can be more prevalent than expect ed before, as noise is practically inevitable in physical systems.