Chaotic Phenomena in a Circuit with a Negative Resistance and an ldeal Switch of Diodes

Naohiko INABA  Toshimichi SAITO  Shinsaku MORI  

IEICE TRANSACTIONS (1976-1990)   Vol.E70   No.8   pp.744-754
Publication Date: 1987/08/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Nonlinear Problems

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It is known that the modified van der Poloscillator proposed by Shinriki et al. can exhibit various interesting phenomena such as a period-doubling-bifurcation, chaos, windows, and a Double Scroll like attractor. But the mechanism of the generation of such phenomena has not yet been explained and cleared. In this paper, it is shown that the phenomena generated in the Shinrikis' circuit could be well explained by a simplified model which we hereafter call as the Ideal System. Here the idealization means that the element of diodes in the circuit operates as an ideal switch. The Ideal System is extremely simple because it contains 3 reactance elements, one linear negative coductance and only one nonlinear element constructed from diodes where the operation of such nonlinear element is very simple. The advantages of using the Ideal System to analyze the mechanism of chaos are as follows: Poincaré map could be derived strictly as a 1-dimensional discrete map from this model and from this obtained Poincaré map, the phenomena could be well explained. Moreover, the theoretical results are verified in the circuit experiments. The Ideal System makes clear the mechanism of chaos gonerated in the circuit.