SIAM Journal of Matrix Analysis and Applications
Eigenvalues, Boundary Conditions (Differential Equations), Matrices
We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary condition.
Veerman, J. J. P., & Hammond, D. K. (2016). Tridiagonal Matrices and Boundary Conditions. SIAM Journal on Matrix Analysis and Applications, 37(1), 1-17.