Research On Pinning And Switching Periodically Intermittent Synchronous Methods Of Complex Networks

In the recent ten years, complex networks have been extensively investigated in various disciplines, including mathematics, physics, computer, biology and social sciences and so on. Synchronization of complex networks not only can well explain many natural phenomena, but also has many potential applications. Moreover, synchronization of complex networks has been a research topic in control field. In view of pinning and periodically intermittent control methods are usual synchronous methods of complex networks, among them, some deep problems need further study, such as the number of pinning nodes, synchronizability by pinning, intermittent synchronous method with variable periods and synchronization of complex networks with delays. For this, some synchronous methods of complex networks and synchronization of complex networks with delays are researched in the dissertation. The main research work is as follows:(1) Synchronous model of complex networks with non-delay and delay couplings is established, which there is time-delay dynamic system on each node. When time-delay dynamic system meets linear condition, synchronous problems of complex networks with simple linear feedback controller and adaptive controller are studied, and the sufficient conditions ensuring synchronization are given, respectively. Then exponential synchronous criteria are derived on the above model when time-delay dynamic system meets the extended decreasing condition. And, numerical simulations are given to verify effectiveness of the synchronous models.(2) Synchronous methods of complex networks by pinning are researched. We analyze sufficient conditions for achieving synchronization, propose a method of adaptive synchronization. And, we find and prove the decreasing law of maximum eigenvalues of the principal sub-matrixes for coupling matrix. On this basis, we give a method for quickly calculating pinning nodes of complex networks, and present the relation among coupling strength, the number of pinning nodes and maximum eigenvalue of the principal sub-matrix for coupling matrix. We also discuss pinning synchronization of directed networks, and get sufficient conditions for achieving synchronization. By finding the relationship between the decreasing speed of maximum eigenvalue sequence of the principal submatrices for coupling matrix and the synchronizability of complex networks by pinning, we discuss the synchronizability of some networks, such as regular networks, random networks, scaie-free networks and small-world networks, and obtain the results that different pinning strategies have different synchronizability. We investigate synchronization problem of complex networks comprised of some sub-networks, and give the relationship between the number of pinning nodes and the number of sub-networks. Moreover, in this paper, synchronous model of complex networks with non-delay and variable delay couplings by pinning is proposed, novel synchronous criteria under adaptive control and linear feedback control are obtained when a function with variable coupling delay meets some conditions. Meanwhile, simulation examples are given to verify effectiveness of the proposed network models.(3) By using periodically intermittent synchronous method, we investigate synchronous model of complex networks with non-delay and delay couplings, whose each node contains a time-delay dynamic system. When neither dynamical system delay nor coupling delay depends on the control width and the non-control width, some exponential synchronous criteria are derived on strict mathematics proofs. Further, we propose the synchronous model of complex networks with non-delay and delay couplings by pinning and switching periodically intermittent synchronous methods. And the conclusion is reached that the controlled network achieves synchronization when the rates of control duration are equal in different periods. At last, a numerical simulation gives effectiveness of synchronization.