Global analysis of crisis in twin-well Duffing system under harmonic excitation in presence of noise

Evolution of a crisis in a twin-well Duffing system under a harmonic excitation in presence of noise is explored in detail by the generalized cell mapping with digraph (GCMD in short) method. System parameters are chosen in the range that there co-exist chaotic attractors and/or chaotic saddles, together with their evolution. Due to noise effects, chaotic attractors and chaotic saddles here are all noisy (random or stochastic) ones, so is the crisis. Thus, noisy crisis happens whenever a noisy chaotic attractor collides with a noisy saddle, whether the latter is chaotic or not. A crisis, which results in sudden appear (or dismissal) of a chaotic attractor, together with its attractive basin, is called a catastrophic one. In addition, a crisis, which just results in sudden change of the size of a chaotic attractor and its attractive basin, is called an explosive one. Our study reveals that noisy catastrophic crisis and noisy explosive crisis often occur alternatively during the evolutionary long run of noisy crisis. Our study also reveals that the generalized cell mapping with digraph method is a powerful tool for global analysis of crisis, capable of providing clear and vivid scenarios of the mechanism of development, occurrence, and evolution of a noisy crisis.