A fuzzy crisis in a Duffing-van der Pol system

被引：7
|
作者：
Hong Ling [1 ]
机构：
[1] Xi An Jiao Tong Univ, MOE Key Lab Strength & Vibrat, Xian 710049, Peoples R China
来源：
CHINESE PHYSICS B | 2010年 / 19卷 / 03期
基金：
中国国家自然科学基金;
关键词：
fuzzy dynamical systems; fuzzy noise; fuzzy bifurcation; cell mapping methods; GLOBAL ANALYSIS; BIFURCATIONS; ATTRACTORS; DYNAMICS;
D O I：
10.1088/1674-1056/19/3/030513
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
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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页数：6
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