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

Abstract

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.