A fuzzy crisis in a Duffing－van der Pol system

doi:10.1088/1674-1056/19/3/030513

中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30513-030513.doi: 10.1088/1674-1056/19/3/030513

A fuzzy crisis in a Duffing－van der Pol system

洪灵

MOE Key Lab for Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2009-06-17 修回日期:2009-08-22 出版日期:2010-03-15 发布日期:2010-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10772140 and 10872155).

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

Received:2009-06-17 Revised:2009-08-22 Online:2010-03-15 Published:2010-03-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10772140 and 10872155).

摘要/Abstract

摘要： 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.

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.

Key words: fuzzy dynamical systems, fuzzy noise, fuzzy bifurcation, cell mapping methods

中图分类号: (Noise)

05.40.Ca

05.45.-a (Nonlinear dynamics and chaos) 02.10.Ab (Logic and set theory)

洪灵. A fuzzy crisis in a Duffing－van der Pol system[J]. 中国物理B, 2010, 19(3): 30513-030513.

Hong Ling(洪灵). A fuzzy crisis in a Duffing－van der Pol system[J]. Chin. Phys. B, 2010, 19(3): 30513-030513.

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A fuzzy crisis in a Duffing－van der Pol system

A fuzzy crisis in a Duffing－van der Pol system

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