﻿ 一阶微分电路构成的混沌

# 一阶微分电路构成的混沌Chaos Structured by First Order Differential Circuit

Abstract: Chaos is the most universally common form of bounded nonlinear function. It commonly exists in the various subject areas of nature. Chaos is the universal term of variously bounded nonlinear aperiodic oscillation. This paper proves that the first order differential circuit which is constituted by mixing of three harmonic sources with different frequency also can produce chaos. It sufficiently explains that the extensiveness of chaotic functions exists in nature. The main harmonic components in the differential equations can be solved by using the harmonic balance principle and power balance theorem. Their correctness of solving results can be verified by phase portrait plotted by simulation. In last century, the era when chaos theory was first published, chaos was considered as a singular attractor in a lot of literatures. The recognition is obviously unilateral and wrong. In fact, people can also make a completely opposite conclusion, the motional trajectory of phase point will neither diverge to be infinite nor converge to stable limit cycle. The phase point freely and arbitrarily wandering in phase space is ordinary and universal motional form, but it is non-random. Chaotic phase portraits on which trajectories are not repeated are pervasive phe-nomenon. The constant periodic oscillation which continuously repeats original orbit is an indi-vidual and special motion form.

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