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A Kolmogorov-Fokker-Planck approach for a stochastic Duffing-van der Pol system

Content Provider	Springer Nature Link
Author	Sharma, Shambhu N.
Copyright Year	2008
Abstract	The stochastic Duffing-van der Pol (SDvdP) system is an appealing case in stochastic system theory, since it involves linear and non-linear vector fields, i.e. system non-linearities, state-independent and state-dependent stochastic accelerations. The equation describing the Duffing-van der Pol system is a second-order non-linear autonomous differential equation. Stochastic estimation procedures, without accounting for possible small stochastic accelerations, may cause an inaccurate estimation of positioning of dynamical systems. In this paper, the estimation-theoretic scenarios of the stochastic version of the Duffing-van der Pol system, which accounts for a state-independent perturbation as well as a state-dependent stochastic perturbation of the order n, where n ≥ 1, is the subject of investigation. This paper discusses the notion of a qualitative analysis for the non-linear stochastic differential system using the Itô differential rule, and subsequently the method is applied to the stochastic system of this paper. This paper develops and explores the efficacy of three different approximate estimation procedures for analyzing the non-linear problem of concern here as well. The theory of the estimation procedures of this paper is developed using the Kolmogorov-Fokker-Planck equation. Numerical simulations involving two different sets of initial conditions are given, since approximate estimation procedures are hard to evaluate theoretically. This paper suggests that the higher-order approximate estimation procedure will lead to the more accurate state estimates.
Starting Page	351
Ending Page	377
Page Count	27
File Format	PDF
ISSN	09713514
Journal	Differential Equations and Dynamical Systems
Volume Number	16
Issue Number	4
e-ISSN	09746870
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-05-16
Publisher Place	India
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Brownian motion Dispersion matrix The Fokker-Planck equation Itô differential rule Stochastic differential equation Stochastic methods Stochastic ordinary differential equations Equations and systems with randomness Computer Science Engineering Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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