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首页> 外文期刊>IEEE Transactions on Circuits and Systems. I, Regular Papers >Qualitative analysis of the dynamics of the time-delayed Chua'scircuit
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Qualitative analysis of the dynamics of the time-delayed Chua'scircuit

机译:时延蔡氏电路动力学的定性分析

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摘要

Several variants of the Chua's circuit have been recently proposed in order to enlarge the class of nonlinear phenomena that can be generated by relatively simple circuits. In particular, Sharkovsky et al. proposed the so called time-delayed Chua's circuit (TDCC), where the original lumped LC resonator is substituted by an ideal transmission line, thereby generating an infinite dimensional system, The TDCC has been studied in details in the absence of the capacitor C, the only lumped dynamic element left in the circuit. This paper studies the effects of the presence of C on the dynamics of the circuit. After recasting the circuit equations in a suitable normalized form, their characteristic equation is theoretically investigated and the regions in the parameter space where all the eigenvalues have negative real part are exactly evaluated along with all the possible qualitative eigenvalue distributions. This analysis allows for a qualitative description of the TDCC dynamics in presence of the capacitor C. In particular, it is shown that, for particular sets of circuit parameters, an even small value of C, e.g., a parasitic element, may completely change the behavior of TDCC and that, on the other hand, any TDCC, exhibiting the period-adding phenomenon for C=0, stilt continues to present this phenomenon even if a small capacitor C is added to the circuit
机译:最近提出了蔡氏电路的几种变型,以扩大可由相对简单的电路产生的非线性现象的种类。特别是,Sharkovsky等。提出了所谓的延时Chua电路(TDCC),其中原始的集总LC谐振器被理想的传输线替代,从而生成了无穷维系统。在没有电容器C的情况下,已经对TDCC进行了详细研究。电路中只剩下集总的动态元件。本文研究了C的存在对电路动力学的影响。在以适当的归一化形式重铸电路方程之后,从理论上研究它们的特征方程,并精确评估参数空间中所有特征值均具有负实部的区域以及所有可能的定性特征值分布。这种分析允许定性描述电容器C存在时的TDCC动态。特别是,对于特定的电路参数集,即使是很小的C值,例如寄生元件,也可能完全改变C值。 TDCC的行为,另一方面,任何出现C = 0的周期增加现象的TDCC,即使向电路中添加了一个小电容器C,踩踏现象仍会继续存在

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