Analysis, Application Of Synchronization And Data Processing In Complex Networks With Randomness

In this dissertation, we mainly discuss three issues concerning analysis of dy-namical behavior and data processing of complex network:synchronization of time varying complex network with randomness, propagation of synchronization signals in neuronal network and data processing of sparse complex network. First, based on the discussion of [14,16,17] on transverse stability of determinist dynamical system, we extend their discussion to random dynamical system and the corresponding results for transverse stability is derived. Then, the derived results above are applied to time vary-ing coupling networks with randomness, conditions about normal Lyapunov exponents is obtained for the synchronization of the coupling networks. After that, we investigate the propagation of synfire chain in the feed-forward neuronal network. The stability of synfire chain is twofold, including the stability of both the synchronisation in the cluster and the asynchronisation out of the cluster. Under the framework of Guassian random filed, we transform the stability of synfire chain to the distribution of attractors of the correlation coefficients by using the moment map. In the end, we discuss the date processing problem. A adaptive Lα(0<a<1) regularization is proposed to extrac-t the potential and valuable information from massive data. Also, the corresponding non-convex optimization algorithm for adaptive Lα(0<a<1) is given to identify the effective neighbor in a sparse complex network. Moreover, based on the theoretical derivation, we introduce a two-stage method to refine the parameter estimation accu-racy. Simulation and real data analysis are given to compare our proposed method to those existing variable selection methods in terms of the accuracy and sparsity.