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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
    Related URLs:
      Depositing user: Mrs Carolynne Westwood
      Date Deposited: 11 Jan 2010 14:19
      Last modified: 04 Sep 2014 23:41
      URI: http://strathprints.strath.ac.uk/id/eprint/13807

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