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Analysing dynamical systems towards computing complete Lyapunov functions

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Version 2 2023-06-12, 08:41
Version 1 2023-06-09, 06:20
conference contribution
posted on 2023-06-12, 08:41 authored by Carlos Argáez, Peter GieslPeter Giesl, Sigurdur Hafstein
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.

Funding

Lyapunov Methods and Stochastic Stability; ICELANDIC RESEARCH FUND; 152429-051

History

Publication status

  • Published

File Version

  • Published version

Journal

Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, 2017, Madrid, Spain

Page range

134-144

Event name

SIMULTECH 2017

Event location

Madrid, Spain

Event type

conference

Event date

26/07/17 - 28/07/17

Place of publication

Madrid, Spain

ISBN

9789897582653

Department affiliated with

  • Physics and Astronomy Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-05-24

First Open Access (FOA) Date

2017-09-01

First Compliant Deposit (FCD) Date

2017-05-24

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