Effects of Small Noise on Implicitly Defined Non-Linear Dynamical Systems

摘要

The dynamics of a large class of non-linear systems are described implicitly, i.e., as a combination of algebraic and differential equations. These dynamics admit of jump behavior. We extend the deterministic theory to a stochastic theory since: (1) the deterministic theory is restrictive; (2) the macroscopic deterministic description of dynamics frequently arises from an aggregation of microscopically fluctuating dynamics; and (3) to robustify the deterministic one in the limit that the intensity of the additive white noise tends to zero. We study the modelling issues involved in applying this stochastic theory to the study of the noise behavior of a multivibrator circuit, discuss the limitations of our methodology for certain classes of systems and present a modified approach for the analysis of sample functions of noisy non-linear circuits.