Fuzzy Cell Mapping
Bifurcations of a Duffing oscillator in the presence of fuzzy noise are studied by means of the fuzzy generalized cell mapping (FGCM) method. The FGCM method is first introduced. Two categories of bifurcations are investigated, namely catastrophic and explosive bifurcations. Fuzzy bifurcations are characterized by topological changes of the attractors of the system, represented by the persistent groups of cells in the context of the FGCM method, and by changes of the steady state membership distribution. The fuzzy noise-induced bifurcations studied herein are not commonly seen in the deterministic systems, and can be well described by the FGCM method. Furthermore, two conjectures are proposed regarding the condition under which the steady state membership distribution of a fuzzy attractor is invariant or not.
This material is based upon work supported by the National Science Foundation under Grant Nos. CMS-0219217 and INT-0217453, and by the Natural Science Foundation of China under Grant Nos. 10772140 and 11172224.
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