3 STEPS TO CHAOS .2. A CHUA CIRCUIT PRIMER

Linear system theory provides an inadequate characterization of sustai ned oscillation in nature. In this two-part exposition of oscillation in piecewise-linear dynamical systems, we guide the reader from linear concepts and simple harmonic motion to nonlinear concepts and chaos. By means of three worked examples, we bridge the gap from the familiar parallel RLC network to exotic nonlinear dynamical phenomena in Chua' s circuit. Our goal is to stimulate the reader to think deeply about t he 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 leas t one locally active resistor, and (3) at least three energy-storage e lements. Chua's circuit is the simplest electronic circuit that satisf ies these criteria. In addition, this remarkable circuit is the only p hysical system for which the presence of chaos has been proved mathema tically. The circuit is readily constructed at low cost using standard electronic components and exhibits a rich variety of bifurcations and chaos. In Part I of this two-part paper, we plot the evolution of our understanding of oscillation from linear concepts and the parallel RL C resonant circuit to piecewise-linear circuits and Chua's circuit. We illustrate by theory, simulation, and laboratory experiment the conce pts of equilibria, stability, local and global behavior, bifurcations, and steady-state solutions. In Part II, we study bifurcations and cha os in a robust practical implementation of Chua's circuit.