The Study Of The Complex Dynamics Networks’ Model And Synchronization

In recent years, with the development of science and technology, the research of complex network has got a big breakthrough. With the deepening of research, people find that the complex network is closely related to many aspects of nature and society. Consequently, it has attracted many attentions of scientists from different research areas.This dissertation discusses the complex network’s development and the research status of its synchronization, introduces several important parameters and several basic complex network models, proposes a new network model called the largest degree limited BA network based on the BA scale-free network model, studies the new network model’s statistical properties, compares the synchronizability of the new model and several basic network models, discusses the characteristics and constructions of cluster network model, studies the synchronous processes of cluster networks in different inter-cluster coupling conditions, and compares the synchronizability of cluster networks in different strategies of adding links between communities. The main research work are as follows:1. In traditional BA scale-free networks, the maximum degree of nodes increases unlimitedly with the scale of networks, which makes a few hub nodes with very large degrees exist in the networks. Considering the cost of constructing the real networks, the maximum degree of nodes will be limited, so on the basis of the growing rules of the BA network, this paper proposes a limited-maximum-degree BA network model, called LBA network. We further study the average path length, clustering coefficient and degree distributions of LBA network under the different values of the restriction of maximum degree K, and compared them with the statistical properties of the neighbor network, the random network and the BA network. Research shows that, the generated LBA network is similar to the neighbor network when K is close to the network average degree, and the LBA network properties are close to the random network when K is about2times the network average degree, and the statistical properties of LBA network are close to the original BA scale-free network with a relative larger K. By taking the network’s nodes as the Kuramoto oscillators, we study the LBA network’s synchronization. Study shows that, the oscillator network’s synchronization increases gradually with the increase of the restriction of maximum degree K, eventually, it will be same as the BA scale-free network’s synchronization.2. By constructing a simple cluster network, we study the synchronous processes of each cluster and the whole cluster network in different inter-cluster coupling conditions. Study shows that, each cluster has a synchronous critical coupling strength value Kc1, the cluster network’s synchronous critical coupling strength value is Krc. If the statistical properties is similar for each cluster, then Kc1is almost equal. When the coupling between clusters is weak, Krc is far greater than Kc1. With the increase of the coupling between clusters, Kc1is almost unchanged, Krc decreases dramatically. Eventually, Krc equals to Kc1and keeps stably, then the network shows unity, the community effectes are vanished. Besides, we study the synchronizability of the cluster network in two different strategies of adding connections between clusters. The first strategy is adding inter-cluster connections randomly, the second one is adding inter-cluster connections with giving the priority to the big nodes. Study shows that, the second stratege is better than the first one for synchronizing the cluster network, since the generating cluster network with using the second strategy has smaller average path length and better synchronizability than the one with using the first strategy.