Figure 3: Stochastic dynamical system with feedback.
From: Stratonovich-to-Itô transition in noisy systems with multiplicative feedback
(a) Schematic representation of a stochastic dynamical system with multiplicative feedback F(y): the driving noise xt (τ=1.1 μs) is multiplied by a function of the system’s state yt. (b) Nominal (dashed line) and experimentally measured (dots) feedback function used in our experiments. (c) Average of 1,000 trajectories for various initial conditions; there is a clear shift of the equilibrium in comparison with the case without feedback (Fig. 2d). (d) Diffusion S(y) (dots) and (e) drift D(y) (dots) of the system status. In (e), the solid line represents the harmonic restoring force G(y) and the dashed line G(y)+0.5S′(y). (f) Agreement between the noise-induced extra-drift ΔD(y) and 0.5S′(y).
