| This work focuses on three aspects of nonlinear circuits and systems: piecewise-linear (PWL) analysis and synthesis techniques, experimental methods for nonlinear dynamics, and theoretical tools for studying neural networks.;In chapter 2, we review the concepts of DC characteristics, the dynamic route, the jump phenomenon, and parasitic dynamics. We show how a clear understanding of these circuit theoretic principles and PWL methods leads to better analysis and synthesis techniques for "hysteretic" electronic circuits.;Chapter 3 addresses design issues for a PWL implementation of Chua's circuit, a simple electronic circuit which exhibits a variety of bifurcation phenomena and attractors.;In chapters 4 and 5, we provide experimental confirmation of the period-adding route to chaos in van der Pol's forced neon bulb relaxation oscillator circuit. We introduce an experimental technique for rapidly and accurately characterizing the Devil's Staircase structure of frequency lockings in periodically forced relaxation oscillators. This technique uses a personal computer, a programmable oscillator, and a frequency counter.;We explain the operation of Tank and Hopfield's linear programming network in chapter 6 by means of the circuit's cocontent function. We drive the DC-equivalence between this circuit and the canonical nonlinear programming circuit of Chua and Lin. In chapter 7, we develop the dynamic nonlinear programming circuit and rigorously analyze its static and dynamic behavior. We show how to guarantee that this neural nonlinear programming network is completely stable. |
