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Stabilization and destabilization of nonlinear differential equations by noise

Appleby, J. and Mao, X. and Rodkina, A. (2008) Stabilization and destabilization of nonlinear differential equations by noise. IEEE Transactions on Automatic Control, 53 (3). pp. 683-691. ISSN 0018-9286

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Abstract

This paper considers the stabilisation and destabilisa- tion by a Brownian noise perturbation which preserves the equilibrium of the ordinary dierential equation x0(t) = f(x(t)). In an extension of earlier work, we lift the restriction that f obeys a global linear bound, and show that when f is locally Lipschitz, a function g can always be found so that the noise perturbation g(X(t)) dB(t) either stabilises an unstable equilibrium, or destabilises a stable equilibrium. When the equilibrium of the deterministic equation is non{hyperbolic, we show that a non{hyperbolic perturbation suffices to change the stability properties of the solution. .

Item type: Article
ID code: 13807
Keywords: brownian motion, almost sure asymptotic stability, It^o's formula, stabilisation, destabilisation, control systems, Probabilities. Mathematical statistics, Mathematics, Control and Systems Engineering, Computer Science Applications, Electrical and Electronic Engineering
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Mrs Carolynne Westwood
Date Deposited: 11 Jan 2010 14:19
Last modified: 17 Jun 2015 21:30
URI: http://strathprints.strath.ac.uk/id/eprint/13807

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