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Discovering forward invariant sets for nonlinear dynamical systems. (English) Zbl 1327.37027
Cojocaru, Monica G. (ed.) et al., Interdisciplinary topics in applied mathematics, modeling and computational science. Selected papers based on the presentations at the 2nd conference, AMMCS 2013, Waterloo, Canada, August 26–30, 2013. Cham: Springer (ISBN 978-3-319-12306-6/hbk; 978-3-319-12307-3/ebook). Springer Proceedings in Mathematics & Statistics 117, 259-264 (2015).
Summary: We describe a numerical technique for discovering forward invariant sets for discrete-time nonlinear dynamical systems. Given a region of interest in the state-space, our technique uses simulation traces originating at states within this region to construct candidate Lyapunov functions, which are in turn used to obtain candidate forward invariant sets. To vet a candidate invariant set, our technique samples a finite number of states from the set and tests them. We derive sufficient conditions on the sample density that formally guarantee that the candidate invariant set is indeed forward invariant. Finally, we present a numerical example illustrating the efficacy of the technique.
For the entire collection see [Zbl 1325.00049].

MSC:
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
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