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 λ1=0<λ2<⋯<λN and null-vector Image 1. 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.
On an inverse tridiagonal eigenvalue problem and its application to synchronization of network motion
Elia, Cinzia;Pugliese, Alessandro
2025-01-01
Abstract
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 λ1=0<λ2<⋯<λN and null-vector Image 1. 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.File in questo prodotto:
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