Article ID Journal Published Year Pages File Type
1898338 Physica D: Nonlinear Phenomena 2006 9 Pages PDF
Abstract

By means of a fuzzy generalized cell mapping method, a Duffing–Van der Pol oscillator in the presence of fuzzy noise is studied in a regime where two symmetrically related fuzzy period-one attractors grow and merge as the intensity of the fuzzy noise is increased. By introducing a small symmetry-breaking parameter to break the symmetry, the merging explosion bifurcation unfolds to a pattern of two catastrophic and explosive bifurcations. Considering both the intensity of the fuzzy noise and the symmetry-breaking parameter together as controls, a codimension two bifurcation of fuzzy attractors is defined, and examples of additive and multiplicative fuzzy noise are given. Such a codimension two bifurcation is fuzzy noise-induced effects which cannot be seen in the deterministic systems.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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