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2011, 2011(Special): 854-863. doi: 10.3934/proc.2011.2011.854

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, Germany

Received  July 2010 Revised  March 2011 Published  October 2011

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.
Keywords: absorption probability, set-oriented method, Domain of attraction, in nitesimal generator, Frobenius-Perron operator.
Mathematics Subject Classification: Primary: 37M99; Secondary: 65P99.
Citation: Péter Koltai. A stochastic approach for computing the domain of attraction without trajectory simulation. Conference Publications, 2011, 2011 (Special) : 854-863. doi: 10.3934/proc.2011.2011.854
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