A fuzzy blue sky catastrophe

In this paper, a blue sky catastrophe of limit cycles of a Van der Pol system with fuzzy disturbances is studied by means of the fuzzy generalized cell mapping (FGCM) method. The blue sky catastrophe happens when a fuzzy limit cycle collides with a fuzzy saddle on the basin boundary as the intensity of fuzzy noise reaches a critical value. The fuzzy limit cycle, characterized by its global topology and membership function, suddenly loses stability and disappears into the blue sky after the collision. We illustrate this bifurcation event by considering the Van der Pol system under the multiplicative fuzzy noise. Such a bifurcation is a fuzzy noise-induced effect which cannot be seen in deterministic systems.