Chaos in piecewise-linear systems

Abstract

A new class of physical systems, those which can be described by piecewise-linear equations, are found to exhibit chaotic behavior similar to that found in previously investigated nonlinear dissipative systems. The example of a damped, sinusoidally forced harmonic oscillator with two possible spring-constant values is investigated in detail. The system exhibits period doubling to chaos characterized by Feigenbaum's universal exponents for a certain range of parameters and an iterated map similar to that in the Lorenz equations for another.