采用振幅耦合方法研究多旋转中心混沌振子的相同步

Study on phase synchronization of chaotic oscillators with many rotational centers based on amplitude coupling

为了找到具有多个旋转中心的混沌系统的相同步与其动力学拓朴变化之间的对应关系 ,采用线性振幅线性耦合方法 ,研究了Lorenz系统和Duffing系统的相同步 ,首先对Lorenz系统和Duffing系统分别进行极坐标变换 ,在线性振幅耦合基础上计算了两个系统的平均旋转数和Lyapunov指数 ,发现 ,随耦合强度的增大 ,系统相同步与系统的Lyapunov指数跃变存在一一对应的关系 ,这表明具有多个旋转中心的混沌系统的相同步与系统动力学拓朴变化也存在着对应关系 .

In order to find some relation between phase synchronization and dynamical topological variation in chaotic systems with many rotational centers,we propose a method of linear amplitude coupling to study the phase synchronization of Lorenz system and Duffing system.First,we convert the original Lorenz system and Duffing system into the dynamics of amplitude and phase.Based on linear amplitude coupling,we calculate the average winding number and Lyapunov exponents.We find that the phase synchronization comes along with the transition of Lyapunov exponents by increasing coupling strength.The results obtained indicate that phase synchronization is definitely related to dynamical topological variation in chaotic systems with many rotational centers.