| A fuzzy crisis in a Duffing-van der Pol system |
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| 作者姓名： | 洪灵 |
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| 作者单位： | MOE Key Lab for Strength and Vibration, Xi'an Jiaotong University,
Xi'an 710049, China |
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| 基金项目： | Project supported by the National
Natural Science Foundation of China (Grant Nos.~10772140 and 10872155). |
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| 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.
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| 关 键 词： | fuzzy dynamical systems fuzzy noise fuzzy bifurcation cell mapping methods |
| 收稿时间： | 2009-06-17 |
A fuzzy crisis in a Duffing－van der Pol system |
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| Hong Ling.A fuzzy crisis in a Duffing-van der Pol system[J].Chinese Physics B,2010,19(3):30513-030513. |
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| Authors: | Hong Ling |
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| Affiliation: | MOE Key Lab for Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, China |
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| 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. |
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| Keywords: | fuzzy dynamical systems fuzzy noise fuzzy bifurcation cell mapping methods |
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