Limit Cycles and Chaos Induced by a Nonlinearity with Memory

Abstract

Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the inverse dissipation rate, we find stable limit cycles. For longer delays, we discover a regime of chaotic dynamics associated with a double scroll attractor. We also analyze the effects of time delay on the spectrum and oscillation amplitude of the oscillator. Our results point to new opportunities for nonlinear energy harvesting, provided that a nonlinearity with distributed time delay can be implemented in mechanical systems.