Study On Synchronization And Percolation Of Complex Networks

As one of the most active areas in the interdisciplinary research field, complex networks attract extensive attentions from researchers of various fields of science and engineering. Many complex systems, from the actual background, such as the Internet, the World Wide Web, the power grid, the railway networks, and so on, can be described by complex dynamical networks. In the last decades, many new concepts and methods have been developed to deal with the structure, function, and evolution of the networks. And the network science has provided the basis for deep understanding of complex systems. Synchronization behavior of complex dynamical networks can well explain many common phenomena in the natural world and the field of engineering. Based on the research of synchronization in complex networks, on one hand, we can understand how topological properties affect synchronous ability, on the other hand, when synchronization is advantaged, we can enhance the synchronous ability of networks, and reduce its negative factors. In addition, the robustness of complex networks has increasingly become an important issue. People make a lot of effort, but still large-scale cascading failures have occurred form time to time. Cascading failure of complex network is defined as one or a few nodes or links failure which will lead more other nodes failure through the coupling relations. Also because complex networks with support- dependence relations exist in the real world, the failing nodes in one network cause nodes in more networks cannot work, and it will cause the chain effect, and lots of nodes failure, even the collapse of the whole network. Therefore, synchronization and percolation analysis of complex networks provide with great theoretical significance and potential applications.The main contents and achievements of this dissertation include:1. Due to limited transimitting speed or network congestion, usually there are time delays in complex networks. Moreover, in real life, there always exsit varies of uncertain information in complex networks, topology identification and parameters identification are still challenging work. Adaptive projective synchronization, between two complex networks with non-delayed and delayed coupling is investigated by the adaptive control method, and this method has been applied to identify the exact topological structure and uncertain parameters of a weighted general complex network.2. Previous studies of synchronization mainly focused on networks under linear coupling. This is, actually, the ideal scenario. Because the information exchange show obvious non-symmetry. The nodes of coupling is not necessarily simple linear. Even in investigations of nonlinear coupled complex networks, there existed a strong assumption on the complex networks:the coupling matrix should be symmetrical. Motivated by these observations, the criteria of impulsive synchronization and global exponential synchronization for nonlinearly coupled complex networks of non-delayed and delayed coupling with asymmetrical matrices are derived.3. The research of percolation on complex networks is related with the investigation of robustness. It is very important both for theoretical research and potential practical application, so it attracts many attentions for academic research. Due to the interdependent relation of many networks in the real world is not mutual or one-to-one corresponding, the research of percolation on partially coupled networks with support-dependence relationship became a hot topic in network science. In this thesis, by theoretical analysis and numerical simulation, we deeply investigated the percolation behavior on the star-like and loop-like networks that with multiple support-dependence relations. It has been found that the percolation has very rich phase transition behaviors, some were never seen in the previous research work.