An approximation for dynamical processes on periodic temporal networks

Abstract

Many dynamical processes such as the spread of epidemic diseases take place on temporal networks. In this paper, we study a special but important case of the temporal networks where the network topology changes periodically in time. We derive the time evolution operator based on the Floquet theory by expanding the periodic Laplacian matrix with respect to the coupling strength. In particular, the first and the second order terms of the expansion are explicitly given with respect to the time integral of the product of the time dependent Laplacian matrices. Using this series expansion, response of the system to a perturbation is also presented. In particular, the deviation from the fast switching approximation, which replaces the time dependent Laplacian matrix with its time average, appears in the lowest order term of the expansion.