@inproceedings{d7f5beb410f643699d310e38b0849669,
title = "Middle point reduction of the chain-recurrent set",
abstract = "Describing dynamical systems requires capability to isolate periodic behaviour. In Lyapunov{\textquoteright}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- dimensions. 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.",
keywords = "Algorithm, Chain-recurrent Set, Dynamical Systems, Lyapunov Functions, Mathematics, Programming",
author = "Carlos Arg{\'a}ez and Peter Giesl and Hafstein, \{Sigurdur Freyr\}",
note = "Publisher Copyright: Copyright {\textcopyright} 2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved.; 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2019 ; Conference date: 29-07-2019 Through 31-07-2019",
year = "2019",
doi = "10.5220/0007920601410152",
language = "English",
series = "SIMULTECH 2019 - Proceedings of the 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications",
publisher = "SciTePress",
pages = "141--152",
editor = "Mohammad Obaidat and Tuncer Oren and Helena Szczerbicka",
booktitle = "SIMULTECH 2019 - Proceedings of the 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications",
}