Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894365 | Chaos, Solitons & Fractals | 2006 | 10 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Ling Hong, Jian-Qiao Sun,