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Authors: Carlos Argáez 1 ; Sigurdur Hafstein 1 and Peter Giesl 2

Affiliations: 1 University of Iceland, Iceland ; 2 University of Sussex, United Kingdom

ISBN: 978-989-758-265-3

Keyword(s): Dynamical System, Complete Lyapunov Function, Meshless Collocation, Radial Basis Functions.

Related Ontology Subjects/Areas/Topics: Dynamical Systems Models and Methods ; Formal Methods ; Mathematical Simulation ; Non-Linear Systems ; Simulation and Modeling

Abstract: Ordinary differential equations arise in a variety of applications, including e.g. climate systems, and can exhibit complicated dynamical behaviour. Complete Lyapunov functions can capture this behaviour by dividing the phase space into the chain-recurrent set, determining the long-time behaviour, and the transient part, where solutions pass through. In this paper, we present an algorithm to construct complete Lyapunov functions. It is based on mesh-free numerical approximation and uses the failure of convergence in certain areas to determine the chain-recurrent set. The algorithm is applied to three examples and is able to determine attractors and repellers, including periodic orbits and homoclinic orbits.

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Paper citation in several formats:
Argáez C., Hafstein S. and Giesl P. (2017). Analysing Dynamical Systems - Towards Computing Complete Lyapunov Functions.In Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-265-3, pages 134-144. DOI: 10.5220/0006440601340144

@conference{simultech17,
author={Carlos Argáez and Sigurdur Hafstein and Peter Giesl},
title={Analysing Dynamical Systems - Towards Computing Complete Lyapunov Functions},
booktitle={Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2017},
pages={134-144},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006440601340144},
isbn={978-989-758-265-3},
}

TY - CONF

JO - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Analysing Dynamical Systems - Towards Computing Complete Lyapunov Functions
SN - 978-989-758-265-3
AU - Argáez C.
AU - Hafstein S.
AU - Giesl P.
PY - 2017
SP - 134
EP - 144
DO - 10.5220/0006440601340144

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