Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2174
Title: Determination of the stationary state densities of the stochastic nonlinear dynamical systems
Authors: Günel, Serkan
Savacı, Ferit Acar
Keywords: Stochastic control systems
Compactly supported multivariable polynomials
Fokker-Planck-Kolmogorov equation
Random dynamical systems
Publisher: Elsevier Ltd.
Source: Günel, S., and Savacı, F. A. (2006). Determination of the stationary state densities of the stochastic nonlinear dynamical systems. International Journal of Engineering Science, 44(18-19), 1432-1447. doi:10.1016/j.ijengsci.2006.06.012
Abstract: The stationary state probability densities appear not only in the study of dynamical systems with random vector fields, but also in the deterministic dynamical systems exhibiting chaotic behavior when the uncertainties in the initial conditions are represented with the probability densities. But since it is very hard problem to determine these densities, in this paper the new efficient method to obtain an approximate solution of Fokker-Planck-Kolmogorov equation which arises in the determination of the stationary state probability densities has been given by representing the densities with compactly supported functions. With specific choice of the compactly supported functions as piecewise multivariable polynomials which are supported on the ellipsoidal regions, the parameters to be calculated for determining the densities can be considerably decreased compared to Multi-Gaussian Closure scheme, in which the stationary densities are assumed to be the weighted average of the Gaussian densities. The main motivation to choose the compactly supported functions is that, in the chaotic dynamics the states are trapped in a specific compact subspace of the state space. The stationary state densities of two basic examples commonly considered in the literature have been estimated using the Parzen's estimator, and the densities obtained using the newly proposed method have been compared with these estimated densities and the densities obtained with the Multi-Gaussian Closure scheme. The results indicate that the presented compactly supported piecewise polynomial scheme can be successful compared to Multi-Gaussian scheme, when the system is highly nonlinear.
URI: http://doi.org/10.1016/j.ijengsci.2006.06.012
http://hdl.handle.net/11147/2174
ISSN: 0020-7225
0020-7225
Appears in Collections:Electrical - Electronic Engineering / Elektrik - Elektronik Mühendisliği
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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