一种新的三维自治混沌系统

摘要

通过对蔡氏电路的研究,提出了一种新的混沌系统,并对该系统的基本动力学特性进行了深入研究,得到该系统的Lyapunov指数和Lyapunov维数,给出了相图、Lyapunov指数谱、分岔图、Poincaré映射以及功率谱等.利用OrCAD-PSpice软件设计了该新混沌系统的振荡电路并进行了仿真实验.研究结果表明,该系统与蔡氏电路产生的混沌吸引子并不拓扑等价,且该系统的参数变化范围较大,最大Lyapunov指数接近1,数值仿真和电路系统实验仿真具有很好的一致性,证实了该系统的存在性和物理上可实现性.%Based on the study of Chua' s circuit, a novel chaotic system is reported. Basic dynamical properties of the new system are further investigated via theoretical analysis and numerical simulation, including Lyapunov exponent, Lyapunov dimension, portrait diagrams, Lyapunov exponent spectrum, bifurcation diagrams, Poincaré mapping and power spectrum. Finally, an electronic circuit is designed by the Orcad-PSpice softeware to implement the new system. The investigation results show that the new chaotic system has broad parameter regions, an maximum Lyapunov exponent approaching one,and is not topologically equivalent to Chua's circuit. It also shows a good agreement between numerical simulation and circuit experimental simulation, which proves the existence and physical realizability of the new chaotic system.