Mechanical Models of Chua's Circuit

Chua’s circuit (see Fig. 1) is one of the simplest physical models that has been widely investigated by mathematical, numerical and experimental methods. One of the main attractions of Chua’s circuit is that it can be easily built with less than a dozen standard circuit components, and has often been referred to as the poor man’s chaos generator. A mathematical analysis of the global unfolding behavior of Chua’s circuit is given in [Chua, 1993]. Perhaps one of the most important observations is that by adding a linear resistor in series with the inductor in Chua’s circuit, the resulting unfolded Chua’s circuit is topologically equivalent to a 21-parameter family of continuous odd-symmetric, piecewise-linear differential equations in R3. Any vector field belonging to the “unfolded” topologically conjugate family can be transformed (mapped) via a nonsingular linear transformation to an unfolded Chua’s circuit with only seven parameters. In addition, it extends the local concept of unfolding to a global one, where all results are valid for the whole space R3. In other words, any autonomous three-dimensional system characterized by an odd-symmetric, threesegment, continuous, piecewise-linear function can be mapped to an unfolded Chua’s circuit having identical qualitative dynamics. The following question was posed in [Chua, 1993]: Since there are several different third-order circuits (which exhibit strange attractors) composed of a continuous, odd-symmetric, piecewiselinear vector field in R3, does a homeomorphic mapping of such circuits to an unfolded Chua’s circuit exist? If such a homeomorphism exists, the two circuits are said to be equivalent (or topologically conjugate). The unfolded Chua’s circuit is canonical in the sense that the governing equations contain a minimum number of parameters for observing the full generality of dynamical behaviors. In this paper, we will present mechanical and electromechanical device models of Chua’s circuit, as well as of the unfolded Chua’s circuit. The Chua’s circuit is shown in Fig. 1. The governing equations have the form