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Technical Brief

Continuation Method on Cumulant Neglect Equations

[+] Author and Article Information
Edmon Perkins

Assistant Professor, Department of Mechanical Engineering, uburn University, Auburn, AL 36849
edmon@auburn.edu

Timothy Fitzgerald

Assistant Professor, Department of Mechanical Engineering, Gonzaga University, Spokane, WA 99258
fitzgeraldt@gonzaga.edu

1Corresponding author.

ASME doi:10.1115/1.4038895 History: Received July 30, 2017; Revised October 30, 2017

Abstract

For stochastic systems, the Fokker-Planck equation (FPE) is used to describe the system dynamics. The FPE is a partial differential equation, which is a function of all the variable in state space and of time. To solve the FPE, several methods are used, including finite elements, moment neglect methods, and cumulant neglect methods. This paper will study the cumulant neglect equations, which are derived from the FPE. It will be shown that the cumulant neglect method, while being a useful and popular tool for studying the system response, introduces several nonphysical artifacts. This paper extends the continuation method technique, typically employed on nonlinear deterministic systems, to a stochastic system. Employing the continuation method to stochastic systems in this way could further develop a bifurcation theory of stochastic systems.

Copyright (c) 2017 by ASME
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