Study On Stability Of Complex Networks And Pinning Control Based On V-Stability Theory

Since the 90's of the last century, the networks have been related to human beings more and more closely as the result of the highly development of Internet technology. These various kinds of networks, such as Internet, power grids, communication networks, neuron networks, metabolic networks, food webs, social networks, collaboration networks and citation networks have greatly infiltrated every corner of our life and affected the production and life of human society constantly. Therefore, comprehending and making use of all these networks exist in nature and human society, studying the epidemic dynamics of these networks, and realizing the controllability of the networks' dynamical behavior play significant role in promoting and enhancing the level of production and the quality of human life.Nowadays, stability problem becomes the focus which attracts more and more attention in the study on the theory of complex networks. Based on the pinning control and the community structure, the paper makes a further study on Lyapunov V-Stability theory, presents the stability criterion and the pinning control strategy, and solves the stability problem of the complex nonlinear dynamical network finally.The primary results of this thesis are described as follows.1. A review is given on the research contents and current status of the theory of complex networks. The studies on networks' stability and the control strategy have also been summarized.2. V-Stability theory is extended to the stability analysis of the stabilization of complex networks with the homogeneous orbit of an isolated node. The stability problem of the complex network which has uncertain couplings is simplified and converted into determining if the characteristic matrix of the network is negative semi-definite or not via replacing the influences on collective behavior caused by self-dynamics of the nodes by their passivity degrees.3. According to the stability criterion, the pinning control strategy is designed to choose the controlled nodes. Hence the stability problem of uncertain complex network model to a homogeneous orbit of the isolated node is solved. The simulation verifies the results obtained.4. Based on the V-stability theory, the stability of the aggregation network is analyzed for the complex networks with typical community structure. The main methods of finding community structure are introduced. Then a new strategy which designs pinning control strategy after dividing the original network into small communities is proposed. Compared to the common method, the efficiency and practicality of the new strategy are improved in the simulation.5. Some complex network models with typical topologies are studied to determine under which situation the new strategy should be applied to solve the stability problem. A standard for choosing control strategy is given. The simulation verifies that the new pinning control method with the standard can reduce the number of the controlled nodes, avoid the meaningless partition and improve the effectiveness of the strategy.The conclusion and perspective are given at the end of the dissertation.