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

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posted on 2023-06-09, 15:46 authored by Hjortur Bjoernsson, Sigurdur Hafstein, Peter GieslPeter Giesl, Enrico Scalas, Skuli Gudmundsson
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.

Funding

Lyapunov Methods and Stochastic Stability; ICELANDIC RESEARCH FUND; 152429-051

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Discrete and Continuous Dynamical Systems - Series B

ISSN

1531-3492

Publisher

American Institute of Mathematical Sciences

Issue

8

Volume

24

Page range

4247-4269

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications
  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-11-07

First Open Access (FOA) Date

2020-04-01

First Compliant Deposit (FCD) Date

2018-11-06

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