Limit cycles and chaos induced by a nonlinearity with memory

Inspired by the recent observation of memory effects in the nonlinear optical response of a coherently-driven micro-cavity, we investigate the effects of varying the memory time on the dynamics of optical and mechanical resonators. For a memory time that is commensurate with the inverse dissipation rate, both optical and mechanical resonators display stable limit cycles. In this regime, we evidence a cascade of period-doubling bifurcations as the memory time increases. For longer memory times, the mechanical resonator displays a regime of chaotic dynamics associated with a double scroll attractor. We also analyze the effects of the memory time on the spectrum and oscillation amplitude of the oscillator. Our results point to new opportunities for nonlinear energy harvesting, provided that a nonlinearity with memory can be implemented in mechanical systems.