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Chin. Phys. B, 2010, Vol. 19(3): 030513    DOI: 10.1088/1674-1056/19/3/030513
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A fuzzy crisis in a Duffing-van der Pol system

Hong Ling(洪灵)
MOE Key Lab for Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, China
Abstract  A crisis in a Duffing--van del Pol system with fuzzy uncertainties is studied by means of the fuzzy generalised cell mapping (FGCM) method. A crisis happens when two fuzzy attractors collide simultaneously with a fuzzy saddle on the basin boundary as the intensity of fuzzy noise reaches a critical point. The two fuzzy attractors merge discontinuously to form one large fuzzy attractor after a crisis. A fuzzy attractor is characterized by its global topology and membership function. A fuzzy saddle with a complicated pattern of several disjoint segments is observed in phase space. It leads to a discontinuous merging crisis of fuzzy attractors. We illustrate this crisis event by considering a fixed point under additive and multiplicative fuzzy noise. Such a crisis is fuzzy noise-induced effects which cannot be seen in deterministic systems.
Keywords:  fuzzy dynamical systems      fuzzy noise      fuzzy bifurcation      cell mapping methods  
Received:  17 June 2009      Revised:  22 August 2009      Accepted manuscript online: 
PACS:  05.40.Ca (Noise)  
  05.45.-a (Nonlinear dynamics and chaos)  
  02.10.Ab (Logic and set theory)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.~10772140 and 10872155).

Cite this article: 

Hong Ling(洪灵) A fuzzy crisis in a Duffing-van der Pol system 2010 Chin. Phys. B 19 030513

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