Bifurcations of forced oscillators with fuzzy uncertainties by the generalized cell mapping method

In this paper, bifurcations in dynamical systems with fuzzy uncertainties are studied by means of the fuzzy generalized cell mapping (FGCM) method. A bifurcation parameter is modeled as a fuzzy set with a triangular membership function. We first study a boundary crisis resulting from a collision of a fuzzy chaotic attractor with a fuzzy saddle on the basin boundary. The fuzzy chaotic attractor together with its basin of attraction is eradicated as the fuzzy control parameter reaches a critical point. We also show that a saddle-node bifurcation is caused by the collision of a fuzzy period-one attractor with a fuzzy saddle on the basin boundary. The fuzzy attractor together with its basin of attraction suddenly disappears as the fuzzy parameter passes through a critical value.