混沌实验数据处理及仿真

Chaotic characteristic analysis and simulations in Chau's circuit

大学物理实验中混沌实验大多采用观察现象的方法进行,本实验采用蔡氏电路(Chua s circuit)产生混沌行为.在观察不同初始值条件下出现的倍周期分岔、阵发混沌、奇异吸引子等相图及现象的基础上,通过对采集数据进行处理,对负电阻伏安特性进行分段线性拟合,用功率频谱法、计算机仿真方法(龙格-库塔数值积分法)对混沌现象进行描绘,将实验数据与非线性方程组的数值解相结合,呈现出混沌现象的本质.

Chua＇s circuit is the simplest circuit, which can become chaotic. The circuit exhibit rich of dynamic phenomenon, it contairis three energy storage elements only. We illustrate the chaotic of the circuit by observe period 1, period 2, single scroll and double scroll chaos attractors, we obtain the chaotic signal by adjusting the parameters of the circuit . Meanwhile we show how to use computer simulate the conclusion of complex dynamic phenomena. We analyze the frequency spectrum with FFT method and simulate the nonlinear equations by using Runge - Kutta method, We also do the curve fitting with least square method. This approach could be use for reference in university experimental study on Chua＇s circuit.