基于二极管的限幅蔡氏电路实验研究

Experimental Study of Limiting Amplitude Chua's Circuit Based on Diode

根据经典蔡氏电路的数学模型,获得系统各个变量之间的运算关系,利用运算放大器、电阻、电容及二极管等元器件,完成非线性限幅函数的电路设计,实现无电感元件的等效蔡氏电路硬件实验图。结果表明,通过调试电路中电阻值,可以直接从示波器观测到蔡氏电路的三个运动变量,包括周期、单涡卷、双涡卷等运动行为的时序图和相位图。搭建的电路结构简单,学生实验时调试容易,并且由于电路中不含电感元件,实验过程中混沌吸引子的稳定性也明显得到了提高。

Through the backward deduction of the mathematical model of Chua＇s circuit, the operational relationship of the Chua＇s circuit variables is obtianed. The circuit design of the nonlinear limiting function is carried out by operational amplifiers, resistors, capacitors and diodes, and the hardware implementation of the equivalent Chua＇s circuit without inductors is realized. It has been proved from experiment that this method can expand the chaotic production range. When varying the values of resistors, the motions of three variables in Chua＇s circuit can be observed directly through an oscilloscope, including the trajectories in phase plane and time-histories for the periodic motions, single scroll attractors and double scroll attractors. The structure of the designed Chua＇s circuit is simple and it is easy to realize in engineering. Moreover, the stability of the chaotic attractors has been improved significantly for the experimental circuit doesn＇t have inductors.