研究多中心奇异吸引子混沌相位的新方法

New methods to study the phase of chaos with multiple rotating center

对一般混沌轨迹的相位定义进行了研究 ,考虑到大量的混沌运动投影到相平面后不是只有一个转动中心的正规转动 ,给出了两种计算瞬时相位的简单方法 .一种方法称之为直接分解方法 ,它是基于分解的思想 .另一种是切线方法 ,它需要计算轨迹在切空间中的角度 .通过对一些算例结果的比较 ,可以看出这两种方法的优越性 .综合而言 ,切线方法是对任意混沌振动适用的 。

In studying the phase synchronization of chaotic oscillators, the most fundamental is to define a proper phase variable for the chaotic oscillation. The definitions of the phase of a general chaotic trajectory are investigated in this paper. Considering a great deal of chaos whose trajectory projected on a plan is not a proper rotation, we present two simple procedures to get its instantaneous phase. One procedure called the direct - decomposition method is based on the idea of decomposition. The other called the tangency method is implemented by calculating angles in the tangent space. By the comparison of the numerical results for some examples, the advantages of these methods are discussed. In conclusion, the tangency method is proper for any chaotic oscillation and therefore may be widely used in the phase synchronization of chaos.