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Global Unfolding of Chua's Circuit
Leon O. CHUA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E76A
No.5
pp.704734 Publication Date: 1993/05/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Neural Nets,Chaos and Numerics) Category: Chaos and Related Topics Keyword: Chua's circuit, Chua's oscillator, chaos, bifurcation, nonlinear circuits, nonlinear dynamics,
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Summary:
By adding a linear resistor in series with the inductor in Chua's circuit, we obtain a circuit whose state equation is topologically conjugate (i.e., equivalent) to a 21parameter family C of continuous oddsymmetric piecewiselinear equations in R^{3}. In particular, except for a subset of measure zero, every system or vector field belonging to the family C, can be mapped via an explicit nonsingular linear transformation into this circuit, which is uniquely determined by 7 parameters. Since no circuit with less than 7 parameters has this property, this augmented circuit is called an unfolding of Chua's circuitit is analogous to that of "unfolding a vector field" in a small neighborhood of a singular point. Our unfolding, however, is global since it applies to the entire state space R^{3}. The significance of the unfolded Chua's Circuit is that the qualitative dynamics of every autonomous 3rdorder chaotic circuit, system, and differential equation, containing one oddsymmetric 3segment piecewiselinear function can be mapped into this circuit, thereby making their separate analysis unnecessary. This immense power of unification reduces the investigation of the many heretofore unrelated publications on chaotic circuits and systems to the analysis of only one canonical circuit. This unified approach is illustrated by many examples selected from a zoo of more than 30 strange attractors extracted from the literature. In addition, a gallery of 18 strange attractors in full color is included to demonstrate the immensely rich and complex dynamics of this simplest among all chaotic circuits.

