Analysing Dynamical Systems - Towards Computing Complete Lyapunov Functions

Carlos Argáez, Sigurdur Hafstein, Peter Giesl

2017

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.

Paper Citation

in Harvard Style

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

in Bibtex Style

@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},
}

in EndNote Style

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