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Bifurcations of a forced Duffing oscillator in the presence of fuzzy noise by the generalized cell mapping method. (English) Zbl 1185.37206

Summary: Bifurcations of a forced 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.

MSC:

37N35 Dynamical systems in control
37G99 Local and nonlocal bifurcation theory for dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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