On an inverse tridiagonal eigenvalue problem and its application to synchronization of network motion
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909498667433984 |
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| author | Dieci, Luca Elia, Cinzia Pugliese, Alessandro |
| author_facet | Dieci, Luca Elia, Cinzia Pugliese, Alessandro |
| contents | In this work, motivated by the study of stability of the synchronous orbit of a network with tridiagonal Laplacian matrix, we first solve an inverse eigenvalue problem which builds a tridiagonal Laplacian matrix with eigenvalues $λ_1=0<λ_2<\cdots <λ_N$ and null-vector $\boldsymbol{e} = \begin{bmatrix} 1 \\ \vdots \\ 1 \end{bmatrix}$. Then, we show how this result can be used to guarantee -- if possible -- that a synchronous orbit of a connected tridiagonal network associated to the matrix $L$ above is asymptotically stable, in the sense of having an associated negative Master Stability Function (MSF). We further show that there are limitations when we also impose symmetry for $L$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On an inverse tridiagonal eigenvalue problem and its application to synchronization of network motion Dieci, Luca Elia, Cinzia Pugliese, Alessandro Dynamical Systems Numerical Analysis 65F18, 15A18 In this work, motivated by the study of stability of the synchronous orbit of a network with tridiagonal Laplacian matrix, we first solve an inverse eigenvalue problem which builds a tridiagonal Laplacian matrix with eigenvalues $λ_1=0<λ_2<\cdots <λ_N$ and null-vector $\boldsymbol{e} = \begin{bmatrix} 1 \\ \vdots \\ 1 \end{bmatrix}$. Then, we show how this result can be used to guarantee -- if possible -- that a synchronous orbit of a connected tridiagonal network associated to the matrix $L$ above is asymptotically stable, in the sense of having an associated negative Master Stability Function (MSF). We further show that there are limitations when we also impose symmetry for $L$. |
| title | On an inverse tridiagonal eigenvalue problem and its application to synchronization of network motion |
| topic | Dynamical Systems Numerical Analysis 65F18, 15A18 |
| url | https://arxiv.org/abs/2408.01066 |