  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.
