一个超混沌系统的设计与电路实现

Design and circuit implementation of a hyperchaotic system

为了提高超混沌系统的随机性以产生复杂的超混沌信号用于混沌保密通信,通过在一个统一混沌系统中引入一个状态反馈控制器设计一个超混沌系统。利用理论和数值仿真的方法对系统的基本特性,如平衡点及在平衡点的特征值、分形维数、分岔图、Lyapunov指数等进行分析。为验证该系统,利用系统方法设计一个模拟超混沌电路。该设计方法重新标度时间和坐标变量,将状态方程变换为一个无量纲的标准方程,获得了一个确定电路参数的严格公式。实验中观察到了超混沌、混沌、拟周期、周期等动力行为,实验结果与数值仿真结果完全相符。

In order to generate complex hyperchaotic signals for chaotic information engineering, a hyperchaotic system is presented in the paper, which is designed based on a unified chaotic system by introducing a state feedback controller. Some basic properties of this system are further analyzed via theoretical and numerical methods such as equilibrium and eigenvalue of the equilibrium, Lyapunov dimension, bifurcation diagram and Lyapunov exponent. Moreover, a analog hyperchaotic circuit is designed by using systematic method to show the effectiveness of the system. In this method, circuit state equations are written in normalized dimensionless form by rescaling the time and coordinates variables, and accurate formulas of determining circuit parameters are obtained. Hyperchaotic, chaotic, quasi-period and period orbits attractors are shown on oscillograph in experiments. It shows a good agreement between numerical simulations and experimental results.