STABILIZATION OF A NONLINEAR-SYSTEM BY MULTIPLICATIVE NOISE

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 an 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.