Control of deterministic diffusion generated by chaotic dynamical systems through time delayed feedback control

Abstract

Time delayed feedback can control chaotic motion to periodic motion by stabilizing an unstable periodic orbit that is embedded in a chaotic set. The time delayed feedback control method can be applied to a non-stationary stochastic process with Gaussian noise, and it can control the diffusion processes in a stochastic system. In this study, we apply time delayed feedback control to the diffusion processes in systems with noise that is more complicated than Gaussian noise, e.g., diffusions induced by chaotic noise generated by chaotic dynamical systems, a logistic map and a one-dimensional piecewise-linear map.