Crises in Chaotic Pendulum with Fuzzy Uncertainty - Hong, Ling; Jiang, Jun; Sun, Jian-Qiao (Journal of Applied Nonlinear Dynamics, 2026)
Crises in chaotic pendulum in the presence of fuzzy uncertainty are observed by means of the fuzzy generalized cell mapping method. A fuzzy chaotic attractor is characterized by its topology and membership distribution function. A fuzzy crisis implies a simultaneous sudden change both in the topology of a fuzzy chaotic attractor and in its membership distribution. It happens when a fuzzy chaotic attractor collides with a regular or a chaotic saddle. Two types of fuzzy crises are specified, namely, boundary and interior crises. In the case of a fuzzy boundary crisis, a fuzzy chaotic attractor disappears after a collision with a regular saddle on the basin boundary. In the case of a fuzzy interior crisis, a fuzzy chaotic attractor suddenly changes in its size after a collision with a chaotic saddle in the basin interior.