Noise-enhanced Response of Nonlinear Oscillators

Although often considered to be undesirable, noise can produce beneficial effects in a system. Here, the authors discuss two representative nonlinear systems and the influence of noise on the responses of these systems. One of these systems is a set of coupled monostable Duffing oscillators, while the second of these systems is a Rayleigh-Duffing system that has been considered in honor of Dr. Y. Ueda. For the coupled oscillators, it is shown that an appropriately chosen noise addition can be used to localize energy as well as shift energy localization locations. In the case of the Rayleigh-Duffing system, the authors illustrate how the addition of noise to a deterministic input can push the system from a periodic attractor in the case without noise to a “broken-egg attractor” in the case with noise. These representative examples serve to illustrate a range of possible noise-influenced responses, and it is expected that similar as well as a wider range of responses can be expected in other nonlinear systems.