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arXiv · 2408.01066

On an inverse tridiagonal eigenvalue problem and its application to synchronization of network motion

Luca Dieci·Cinzia Elia·Alessandro Pugliese
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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 $\lambda_1=0<\lambda_2<\cdots <\lambda_N$ 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 $L$.

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Luca Dieci, Cinzia Elia, Alessandro Pugliese. 2024-08-02. On an inverse tridiagonal eigenvalue problem and its application to synchronization of network motion. https://arxiv.org/abs/2408.01066

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