A fuzzy crisis in a Duffing-van der Pol system  

作　　者：洪灵 

机构地区：[1]MOE Key Lab for Strength and Vibration,Xi'an Jiaotong University

出　　处：《Chinese Physics B》2010年第3期182-187,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos. 10772140 and 10872155)

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.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.

关 键 词：fuzzy dynamical systems fuzzy noise fuzzy bifurcation cell mapping methods 

分 类 号：O415.5[理学—理论物理]