Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function

Bjoernsson, Hjortur, Hafstein, Sigurdur, Giesl, Peter, Scalas, Enrico and Gudmundsson, Skuli (2019) Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function. Discrete and Continuous Dynamical Systems - Series B, 24 (8). pp. 4247-4269. ISSN 1531-3492

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Abstract

The y-basin of attraction of the zero solution of a nonlinear stochastic differential equation can be determined through a pair of a local and a non-local Lyapunov function. In this paper, we construct a non-local Lyapunov function by solving a second-order PDE using meshless collocation. We provide a-posteriori error estimates which guarantee that the constructed function is indeed a non-local Lyapunov function. Combining this method with the computation of a local Lyapunov function for the linearisation around an equilibrium of the stochastic differential equation in question, a problem which is much more manageable than computing a Lyapunov function in a large area containing the equilibrium, we provide a rigorous estimate of the stochastic y-basin of attraction of the equilibrium.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Alice Jackson
Date Deposited: 07 Nov 2018 15:56
Last Modified: 01 Jul 2019 14:30
URI: http://sro.sussex.ac.uk/id/eprint/80036

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Project NameSussex Project NumberFunderFunder Ref
Lyapunov Methods and Stochastic StabilityUnsetICELANDIC RESEARCH FUND152429-051