由无损耗电路构成的非周期振荡

Aperiodic Oscillation Structured by Lossless Circuit

摘要: 不含耗能元件的自治电路是一个保守系统，其振荡的相图是一个哈密顿圈不是极限环，圈的大小与网络中的初始储能密切相关，起振后网内的总储能始终保持恒定，它是周期振荡但不是吸引子。具有激励源不含耗能元件的非自治电路是一个无损耗系统。振荡解不但与激励源有关，且敏感的依赖于初始条件。每个电抗元件内的储能，在每个激励周期内的变化过程是不同的。其相图的有界性与非周期性，显示混沌振荡的基本特征。本文介绍用无损耗系统构成一个混沌信号发生器的实验电路。论证无损耗系统产生的混沌是一种非周期振荡，它对邻近的轨线没有吸引性，因而它也不是一个吸引子。

Abstract: An autonomous circuit without dissipative elements is a conservative system, whose phase portrait of oscilla- tion is a Hamiltonian cycle rather than a limit cycle. The size of cycle is closed related to the initial energy stored in the network. The total energy stored in the network keeps always constant after the starting instant. It is a periodic oscilla- tion but not an attractor.It is a lossless system that the non-autonomous circuit has excited source but without dissipative elements. The oscillation solution not only depends on the excited source, but also on the initial conditions sensitively. The change process of stored energy of every reactance elements is distinct in every excited period. The boundness and aperiodicity of phase portrai show the basic characteristics of the chaotic oscillation. This paper introduces an experi- mental circuit of chaotic signal generator structured by lossless system. It is demonstrated that the chaos produced by the lossless systems is a kind of aperiodic oscillation. It has not attractiveness for neighboring trajectory so that it is not an attractor either.