混沌振子的广义旋转数和同步混沌的Hopf分岔

GENERALIZED WINDING NUMBER OF CHAOTIC OSCILLATORS AND HOPF BIFURCATION FROM SYNCHRONOUS CHAOS

对应于混沌振子的各个Ｌｙａｐｕｎｏｖ指数，在切空间中定义了广义相位和广义旋转数．广义旋转数和Ｌｙａｐｕｎｏｖ指数相结合，可以更完整地描述混沌吸引子的各个运动模式的运动特征，包括伸缩与旋转．用耦合Ｄｕｆｉｎｇ振子研究了时空混沌系统在同步混沌失稳时发生的分岔行为．结果表明，耦合振子的同步混沌态可以发生一种Ｈｏｐｆ分岔，在Ｈｏｐｆ分岔后，系统的功率谱中出现了一个特征频率，其值恰好等于分岔前临界横模的广义旋转数．

Abstract 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.