A Crisis with a Special Scaling Behavior

Abstract

A kind of crisis with special scaling properties has been observed in a discontinuous map. The crisis happens via a collision between a discontinuity of the mapping function and an unstable periodic orbit locating on the basin boundary of the chaotic attractor. The scaling property of the crisis is ⟨τ⟩ ∝ ϵ-1.8, where ⟨τ⟩ and ϵ stand for the average characteristic time and the control parameter value crossing the critical point, respectively.