Stabilization of a nonlinear system by multiplicative noise

Abstract

The effect of multiplicative colored noise on the stabilization of a bistable system is studied numerically. In particular, numerical simulation of a much discussed theoretical study carried out by Graham and Schenzle [Phys. Rev. A 26, 1676 (1982)] is presented. To corroborate this study, analog simulation studies have been undertaken to date which concluded that there are substantial limitations of the theory. Subsequently, to commensurate with those numerical studies, a variant theoretical interpretation was also made. On the other hand, it is also discussed in the literature that the inherent presence of weak additive stochastic forces in analog-simulation measurements may have prevented the substantiation of the theory. With the present status thus being inconclusive, in this Rapid Communication digital-simulation results are presented that provide a variant perspective for the theoretical study. Importantly, the study also sheds new light on the old controversies: interpretation of Stratonovich and Ito calculi and adiabatic elimination. It is also pointed out that contrary to existing notion in the literature—that digital simulation is biased on the algorithm selected (Ito or Stratonovich)—one algorithm is capable of distinguishing the two interpretations. And this is possible due to the inclusion of inertia in the formulation by Graham and Schenzle.