Analysis the convergency speed of estimating the network topology based on the dynamical synchronization

Abstract

Identifying convergent speed is an important but rarely discussed problem in estimating topologies of complex networks. In this paper, we discuss this problem mainly in both weakly and strongly coupled conditions. In the weakly coupled conditions, the convergent speed we defined increases linearly with coupling strength increasing. After analyzing the dynamics, we find that this relation is universal. In light of the repeatedly driving method we proposed recently, we generalize the definition of the convergent speed into the area of synchronization. In this case, there is a best length of the driving time series to maximize the convergent speed. The knowledge of convergent speed helps us understand the topological information embedded in the time series.