Eigenpairs for the Analysis of Complete Lyapunov Functions

被引：0

作者：

Argaez, Carlos ^{[1
]}

Giesl, Peter ^{[2
]}

Hafstein, Sigurdur Freyr ^{[3
]}

机构：

[1] Marine & Freshwater Res Inst, Fornubuoir 5, IS-220 Hafnarfjorour, Iceland

[2] Univ Iceland, Sci Inst, Dunhagi 3, IS-107 Reykjavik, Iceland

[3] Univ Sussex, Dept Math, Falmer BN1 9QH, England

来源：

COMPLEXITY | 2022年 / 2022卷

关键词：

D O I：

10.1155/2022/3160052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 study, 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.

引用

页数：17

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