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The Approximate Solutions of FPK Equations in High Dimensions for Some Nonlinear Stochastic Dynamic Systems

Published online by Cambridge University Press:  20 August 2015

Guo-Kang Er  and
Vai Pan Iu
Guo-Kang Er*
Affiliation:
Faculty of Science and Technology, University of Macau, Macau SAR, P. R. China
Vai Pan Iu*
Affiliation:
Faculty of Science and Technology, University of Macau, Macau SAR, P. R. China
*
Corresponding author.Email:gker@umac.mo
Email:vaipaniu@umac.mo
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Abstract

The probabilistic solutions of the nonlinear stochastic dynamic (NSD) systems with polynomial type of nonlinearity are investigated with the subspace-EPC method. The space of the state variables of large-scale nonlinear stochastic dynamic system excited by white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system is then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in another subspace is formulated. Therefore, the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of large-scale NSD systems solvable with the exponential polynomial closure method. Examples about the NSD systems with polynomial type of nonlinearity are given to show the effectiveness of the subspace-EPC method in these cases.

Keywords

05.10.Gg05.10.-a02.30.JrNonlinear stochastic dynamic systemslarge-scale systemsprobability density functionFokker-Planck-Kolmogorov equationsubspace
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 5 , November 2011 , pp. 1241 - 1256
Copyright
Copyright © Global Science Press Limited 2011

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