一个具有完全四翼形式的四维混沌

本文通过引进一个非线性状态反馈控制器, 提出了一个新的四维混沌系统, 该混沌吸引子能在任何方向上都表现出四翼形式. 由于存在一个大的正李雅普诺夫指数, 混沌系统具有一些非常有趣和复杂的动力学行为. 对系统的一些基本动力学特性进行了数值模拟和理论分析, 如平衡点、耗散性、Poincaré映射、频谱、时域谱和混沌行为等. 通过对Lyapunov指数谱和分岔图的分析, 进一步研究了混沌行为的系统参数敏感性. 最后, 设计了一个实现四翼混沌系统的振荡电路, EWB观察结果与数值模拟结果具有良好的一致性.

A 4-D chaos with fully qualified four-wing type

In this paper we propose a new simple four-dimensional (4D) chaotic system by introducing a nonlinear state feedback controller. There is a fully qualified four-wing type in all directions of the chaotic attractor. With a larger positive Lyapunov exponent, some interesting and complex dynamic behaviors are obtained. Basic dynamical properties of the four-wing attractor are studied by numerical and theoretical analyses, such as dissipativity equilibria, Poincaré map, spectrum map, continuous spectrum and chaotic behaviors. The sensitivities of system parameters to the chaotic behaviors are further explored by calculating, in detail, its Lyapunov exponent spectrum and bifurcation diagrams. Finally, an oscillator circuit is designed for implementation. The EWB observation results are in reasonable agreement with the numerical simulation results.