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Fuzzy Codimension Two Bifurcations

[+] Author Affiliations
Ling Hong

Xi’an Jiaotong University, Xi’an, Shaanxi, China

Jian-Qiao Sun

University of California at Merced, Merced, CA

Paper No. DETC2011-47249, pp. 601-608; 8 pages
doi:10.1115/DETC2011-47249
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5478-5
  • Copyright © 2011 by ASME

abstract

By means of 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 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 fuzzy noise and the symmetry-breaking parameter together as controls, a codimension two bifurcation of fuzzy attractors is defined, and two 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.

Copyright © 2011 by ASME
Topics: Bifurcation

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