Open AccessGENERALIZED WINDING NUMBER OF CHAOTIC OSCILLATORS AND HOPF BIFURCATION FROM SYNCHRONOUS CHAOS
Author(s) -
Ma Wen-Qi,
Yang Jun-Zhong,
Liu Wen-Ji,
Gang Bao,
Gang Hu
Publication year - 1999
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.48.787
Subject(s) - saddle node bifurcation , mathematics , lyapunov exponent , hopf bifurcation , biological applications of bifurcation theory , period doubling bifurcation , chaotic , bifurcation , bifurcation diagram , attractor , pitchfork bifurcation , homoclinic bifurcation , transcritical bifurcation , bogdanov–takens bifurcation , mathematical analysis , control theory (sociology) , physics , nonlinear system , quantum mechanics , computer science , control (management) , artificial intelligence
In describing various modes of chaotic oscillators, generalized winding numbers are defined in tangent space corresponding to Lyapunov exponents of the chaotic attractor. Bifurcation behaviors from synchronous chaos of coupled Duffing oscillators are investigated using these concepts. The results show that a kind of Hopf bifurcation can take place from the synchronous chaotic state. Analysis of power spectrum indicates that the characteristic frequency created by the Hopf bifurcation is equal to the generalized winding number of the critical transverse modes just before the bifurcation.