Finding Response Cumulants for Nonlinear Systems With Multiplicative Excitations

Abstract

A relatively straightforward formulation is presented for deriving the differential equations governing the evolution of the response cumulants and moments of a dynamical system. This is a very general framework which applies to linear and nonlinear systems subjected to external and multiplicative non-Gaussian, delta-correlated processes. This formulation provides an alternative to both the partial differential Fokker Planck equation that has sometimes been used in deriving moment or cumulant equations, and the differential (as opposed to derivative) relationships of the Itô calculus. It is believed that many analysts may find the technique used here to be more obvious than the alternatives, since the derivative relationships for the stochastic process are of the same form as in the more familiar ordinary differential equations.

Additional details