Generalized winding number of chaotic oscillators and Hopf bifurcation from synchronous chaos

In describing various modes of chaotic oscillators, generalized winding num bers are defined in tangent space corresponding to Lyapunov exponents of th e chaotic attractor. Bifurcation behaviors from synchronous chaos of couple d Duffing oscillators are investigated using these concepts. The results sh ow that a kind of Hopf bifurcation can take place from the synchronous chao tic state. Analysis of power spectrum indicates that the characteristic fre quency created by the Hopf bifurcation is equal to the generalized winding number of the critical transverse modes just before the bifurcation.