Eigenpairs for the analysis of complete Lyapunov functions

Argáez, Carlos, Giesl, Peter and Freyr Hafstein, Sigurdur (2022) Eigenpairs for the analysis of complete Lyapunov functions. Complexity. ISSN 1076-2787 (Accepted)

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Abstract

A complete Lyapunov function describes the qualitative behaviour of a dynamical system: the areas where the orbital derivative vanishes and where it is strictly negative, characterise the chain recurrent set and the gradient-like flow, respectively. Moreover, its local maxima and minima show the stability properties of the connected components of the chain recurrent set. In this article, we use collocation with radial basis functions to numerically compute approximations to complete Lyapunov functions, and then localise and analyse the stability properties of the connected components of the chain recurrent set using its gradient and Hessian. In particular, we improve the estimation of the chain recurrent set and we determine the dimension and the stability properties of its connected components.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 23 Jun 2022 17:42
Last Modified: 24 Jun 2022 07:01
URI: http://sro.sussex.ac.uk/id/eprint/106584

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