A novel chaotic attractor with constant Lyapunov exponent spectrum and its circuit implementation

Abstract

Based on the further evolvement of the improved chaotic system with constant Lyapunov exponent spectrum, by introducing an absolute term in the dynamic equation, a novel chaotic attractor is found in this paper. Firsty, the existence of chaotic attractor is verified by simulation of phase portrait, Poincaré mapping, and Lyapunov exponent spectrum. Secondly, the basic dynamical behaviour of the new system is investigated and expounded. Simulation of Lyapunov exponent spectrum, bifurcation diagram and numerical analysis on amplitude evolvement of state variables show that the state variables of the chaotic system can be modified linearly by a global linear amplitude adjuster while the Lyapunov exponent spectrum keeps on stable and the chaotic attractor displays the same phase portrait. Finally, an analog circuit is designed to implement the new system, the chaotic attractor is observed and the action of global linear amplitude adjuster is verified, all of which show a good agreement between numerical simulation and experimental results.