耦合Lorenz振子的同步混沌分岔

Hopf Bifurcation from Synchronous Chaos of Coupled Lorenz Oscillators

研究了时空混沌系统--耦合Lorenz振子同步混沌的分岔行为.当非对称耦合参数达到临界值,耦合系统的同步混沌态发生Hopf分岔,在同步混沌态上迭加一个周期行波.分岔点的参数可由计算Lyapunov指数得到,分岔产生的行波频率等于分岔前临界横模的广义旋转数.继续增加非对称耦合参数,系统经历准周期、混沌到周期运动的变化.在这个过程中同步混沌发生Hopf分岔时产生的周期行波始终存在.

A new kind of Hopf bifurcation from synchronous chaos of a spatiotemperal system was present composed of coupled Lorenz oscillators. When the asymmetric coupling parameter reached a critical value, a Hopf bifurcation from the synchronous chaos takes place. As a result, a periodic traveling wave is superposed on the synchronous chaotic state. The bifurcation threshold of the parameter can be obtained from the Lyapunov exponent spectrum. The frequency of the traveling wave is equal to the generalized winding number of the critical transverse modes. As the asymmetry of coupling is enhanced, the system undergoes quasiperiodic, chaotic and periodic motions. All the time the traveling wave in the process produced from Hopf bifurcation is maintained.