Eigenpairs for the Analysis of Complete Lyapunov Functions
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 stab...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/3160052 |
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| author | Carlos Argáez Peter Giesl Sigurdur Freyr Hafstein |
| author_facet | Carlos Argáez Peter Giesl Sigurdur Freyr Hafstein |
| author_sort | Carlos Argáez |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-550650023d80477e92f3b33542371c00 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-550650023d80477e92f3b33542371c002025-02-03T01:22:39ZengWileyComplexity1099-05262022-01-01202210.1155/2022/3160052Eigenpairs for the Analysis of Complete Lyapunov FunctionsCarlos Argáez0Peter Giesl1Sigurdur Freyr Hafstein2Marine and Freshwater Research InstituteScience InstituteDepartment of MathematicsA 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.http://dx.doi.org/10.1155/2022/3160052 |
| spellingShingle | Carlos Argáez Peter Giesl Sigurdur Freyr Hafstein Eigenpairs for the Analysis of Complete Lyapunov Functions Complexity |
| title | Eigenpairs for the Analysis of Complete Lyapunov Functions |
| title_full | Eigenpairs for the Analysis of Complete Lyapunov Functions |
| title_fullStr | Eigenpairs for the Analysis of Complete Lyapunov Functions |
| title_full_unstemmed | Eigenpairs for the Analysis of Complete Lyapunov Functions |
| title_short | Eigenpairs for the Analysis of Complete Lyapunov Functions |
| title_sort | eigenpairs for the analysis of complete lyapunov functions |
| url | http://dx.doi.org/10.1155/2022/3160052 |
| work_keys_str_mv | AT carlosargaez eigenpairsfortheanalysisofcompletelyapunovfunctions AT petergiesl eigenpairsfortheanalysisofcompletelyapunovfunctions AT sigurdurfreyrhafstein eigenpairsfortheanalysisofcompletelyapunovfunctions |