一种恒Lyapunov指数谱混沌吸引子及其Jerk电路实现

An attractor with invariable Lyapunov exponent spectrum and its Jerk circuit implementation

基于Colpitts方程,提出了一种新的三维混沌吸引子.该混沌吸引子在系统变幅参数改变时,输出混沌信号中的两维信号的幅值随着参数作线性变化,第三维信号的幅值保持在同样的数值区间,而系统的Lyapunov指数谱却保持恒定.该混沌系统通过改造Colpitts混沌系统归一化方程中的指数项为绝对值项而得到.通过相图、庞加莱映射、功率谱以及Lyapunov指数,证明了该混沌吸引子的存在性.对这种新型混沌吸引子的基本动力学行为予以分析,基于Lyapunov指数谱阐述并论证了该系统能够呈现周期态和混沌态.最后,给出该特殊的混沌吸引子的Jerk函数实现电路.系统的混沌特性与某个特定参数无关而信号幅值却随之线性改变的重要特性,使得该系统在混沌雷达、保密通信以及其他信息处理系统中具有潜在的重大应用价值.

A novel three-dimensional chaotic attractor derived from Colpitts equation is proposed in this paper. When the given parameter varies in a broad range, the amplitude of the singals of the first two dimensions changes linearitly while the third one keeps its amplitude in the same range. At the same time, the Lyapunov exponent spectrum keeps invariable. This chaotic system is developed by substituting the absolute term for the exponent term in normalized Colpitts equation. Lyapunov exponent, Poincaré mapping, phase portrait and spectrum are given to verify that the attractors are chaotic. In addition, some basic dynamical characteristics of the new system are investigated briefly. Based on Lyapunov exponent spectrum analysis, it is demonstrated that the new system can go into periodic and chaotic behaviors. At last, the Jerk function of the new system is put forward and its circuit implementation is designed. The feature that the chaotic characteristic of this system has nothing to do with the given parameter while the amplitude of some state variables can be changed linearly makes it reasonable to predict that the chaotic system will have tremendous potential applications in chaotic radar, secure communications and other information processing systems.