Characteristic crisis in a system with distinguishable strong and weak dissipation functions

Abstract

This article reports a crisis in a system described by a concatenation of a conservative and a dissipative mapping. The special feature of the crisis lies in its special escaping hole. A fat fractal forbidden net, induced by interaction between discontinuous and noninvertible properties, introduces rippled-like attraction basins of two periodic attractors, which appear after the crisis when a chaotic attractor suddenly loses stability. There are small areas, which serve as escaping holes and are dominated by strong dissipation as well as confined by the boundary of forbidden region only in the vicinity of each periodic point. To our knowledge, the crisis has not been reported before.