A stochastic approach for computing the domain of attraction without trajectory simulation

Péter Koltai

doi:10.3934/proc.2011.2011.854

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2011, Volume 2011: 854-863. Doi: 10.3934/proc.2011.2011.854 open access

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A stochastic approach for computing the domain of attraction without trajectory simulation

Péter Koltai^1,

1.
Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3., 85748 Garching bei München

Received: June 30, 2010

Revised: February 28, 2011

Published: August 2017

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Abstract

We present an approach for the numerical computation of the domain of attraction of some asymptotically stable set for continuous-time autonomous systems. It is based on a set-oriented approximation of the original dynamical system by a Markov jump process. The domain of attraction is extracted from absorption probabilities of the jump process. The method does not perform any trajectory simulation, integrals of the underlying vector eld on the boundary of partition elements are computed instead.

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Mathematics Subject Classification: Primary: 37M99; Secondary: 65P99.

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