Middle Point Reduction of the Chain-recurrent Set

Carlos Argáez, Peter Giesl, Sigurdur Hafstein

Abstract

Describing dynamical systems requires capability to isolate periodic behaviour. In Lyapunov’s theory, the qualitative behaviour of a dynamical system given by a differential equation can be described by a scalar function that decreases along solutions: the Complete Lyapunov Function. The chain-recurrent set will produce constant values of an associated complete Lyapunov function and zero values of its orbital derivative. Recently, we have managed to isolate the chain-recurrent set of different dynamical systems in 2- and 3-di- mensions. An overestimation, however, is always obtained. In this paper, we present a method to reduce such overestimation based on geometrical middle points for 2-dimensional systems.

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Paper Citation


in Harvard Style

Argáez C., Giesl P. and Hafstein S. (2019). Middle Point Reduction of the Chain-recurrent Set.In Proceedings of the 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-381-0, pages 141-152. DOI: 10.5220/0007920601410152


in Bibtex Style

@conference{simultech19,
author={Carlos Argáez and Peter Giesl and Sigurdur Hafstein},
title={Middle Point Reduction of the Chain-recurrent Set},
booktitle={Proceedings of the 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2019},
pages={141-152},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007920601410152},
isbn={978-989-758-381-0},
}


in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Middle Point Reduction of the Chain-recurrent Set
SN - 978-989-758-381-0
AU - Argáez C.
AU - Giesl P.
AU - Hafstein S.
PY - 2019
SP - 141
EP - 152
DO - 10.5220/0007920601410152