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Iterative Construction of Complete Lyapunov Functions: Analysis of Algorithm Efficiency

  • Carlos ArgáezEmail author
  • Peter Giesl
  • Sigurdur Hafstein
Conference paper
First Online:
  • 136 Downloads
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 947)

Abstract

Differential equations describe many interesting phenomena arising from various disciplines. This includes many important models, e.g. predator-prey in population biology or the Van der Pol oscillator in electrical engineering. Complete Lyapunov functions allow for the systematic study of the qualitative behaviour of complicated systems. In this paper, we extend the analysis of the algorithm presented in [1]. We study the efficiency of our algorithm and discuss important sections of the code.

Keywords

Dynamical system Complete Lyapunov function Orbital derivative Meshless collocation Radial Basis Functions Algorithms Scalability 
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Notes

Acknowledgement

First author wants to thank Dr. A. Argáez for nice discussions on normed spaces as well as the Icelandic Research Fund (Rannís) for funding this work under the grant: number 163074-052, Complete Lyapunov functions: Efficient numerical computation.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Science InstituteUniversity of IcelandReykjavíkIceland
  2. 2.Department of MathematicsUniversity of SussexBrightonUK

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