Abstract
Chaos has been widely reported and studied in Chua's circuit family, which is characterized by a 21 parameter family of odd-symmetric piecewise-linear vector fields in R3. In this tutorial paper, we shall prove that, up to a topological equivalence, all the dynamics of this family are subsumed within that of a single circuit: Chua's oscillator; directly derived from Chua's circuit by adding a resistor in series with the inductor. We provide explicit formulas of the parameters of Chua's oscillator leading to a behavior qualitatively identical to that of any system belonging to Chua's circuit family. These formulas are then used to construct, in an almost trivial way, a gallery of (quasiperiodic and strange) attractors belonging to Chua's circuit family. A user-friendly program is available to allow a better understanding of the evolution of the dynamics as a function of the parameters of Chua's oscillator, and to follow the trajectory in the eigenspaces.
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