一个新的四维混沌系统理论分析与电路实现

分析了一个新的复杂的四维混沌系统的基本特性，该系统每个方程中包含一个三次交叉乘积项，共有9个平衡点，它们相对于原点和坐标轴具有完美的对称性，并且相对于线性特性和不变流形具有很好的相似性.描述了两个同时共存的对称双翼吸引子.最后，设计了一个模拟电路来实现这个新的四维混沌系统，表明数值仿真和电路实现具有很好的一致性，同时说明在应用上由于频率不同导致的仿真与物理实现之间的重要区别. 关键词： 四维混沌系统 Lyapunov 指数 共存双翼吸引子 电路实现

Theoretical analysis and circuit implementation of a new four dimensional chaotic system

This paper further analyzes some basic properties of a new complex four-dimensional continuous autonomous chaotic system, in which each equation contains a cubic cross-product term. The new system has 9 equilibria which display graceful symmetry with respect to the origin and coordinate planes, and they are similar with respect to their linearized characteristics and invariant manifolds. Two coexisting symmetric double-wing chaotic attractors are described. Finally, an analog circuit is designed to implement the new system, which shows a good agreement between numerical simulation and experimental results, and explains their significant distinction in applications due to difference in frequencies.