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

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 < ⋯ < λ N and null-vector . 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 .