Three steps to chaos. II. A Chua´s circuit primer

For Pt. I see ibid., vol. 40, no. 10, p. 640, 1993. Linear system-theory provides an inadequate characterization of sustained oscillation in nature. This two-part exposition of oscillation in piecewise-linear dynamical systems, guides the reader from linear concepts and simple harmonic motion to nonlinear concepts and chaos. By means of three worked examples, the authors bridge the gap from the familiar parallel RLC network to exotic nonlinear dynamical phenomena in Chua´s circuit. The goal is to stimulate the reader to think deeply about the fundamental nature of oscillation and to develop intuition into the chaos-producing mechanisms of nonlinear dynamics. In order to exhibit chaos, an autonomous circuit consisting of resistors, capacitors, and inductors must contain (1) at least one nonlinear element, (2) at least one locally active resistor, and (3) at least three energy-storage elements. Chua´s circuit is the simplest electronic circuit that satisfies these criteria. In addition, this remarkable circuit is the only physical system for which the presence of chaos has been proved mathematically. The circuit is readily constructed at low cost using standard electronic components and exhibits a rich variety of bifurcations and chaos. Part II in this series studies bifurcations and chaos in a robust practical implementation of Chua´s circuit