Synchronizability Of Deterministic Networks Based On Spectrum Calculations

Synchronizability of a network quantified by the spectrum has attracted increasing attention with a focus on the interplay between network topology and synchronizability.Presently the studies of synchronizability have been investigated by numerical simulations and there is lack of rigorous theoretical analysis on the exact relationship between them.Since the deterministic networks have regular topological structures,their advantage is that analytical results of network topology and dynamics could be obtained.Therefore,this dissertation selects many types of deterministic networks as network models.Through calculating the spectrum of the considered networks,the exact solutions regarding the synchronizability with respect to network parameters are obtained.Finally,the impact of network parameters on the synchronizability is studied.The detailed works are as follows:The synchronizability of ring trees and tree networks with same number of nodes is compared.Using the methods of spectrum and network topology,the accurate spectra are obtained and the relationship between the synchronizability(bounded and unbounded synchronous region)and network parameters is investigated.Under the same network scale in a generation,the synchronizability of tree networks is stronger than the ring trees.The impact of node failures on the synchronizability is studied.The windmill network is chosen as the network model.Through the matrix operations and different node failures forms,the analytical solutions of the synchronizability are obtained and their impacts on the synchronizability are correspondingly studied.The obtained results show that the synchronizability is related to the number of node failures.The synchronizability of unidirectionally coupled multi-layer star networks is analyzed.By constructing a multi-layer coupled network model,the exact results of the synchronizability against the number of layers and coupling strength are obtained.For the unbounded synchronous region,the synchronizability has a positive correlation with the coupling strength.While for the bounded synchronous region,the synchronizability has a negative correlation with the number of layers and nodes,and the coupling strength between the inter-layer central nodes.