| The human society has gradually entered an Internet age along with a rapid development of computer and information technology since the well-known small-world network and scale-free network were presented and studied penetratingly by Watts and Barabasi et al.. So far, the studies of complex networks have penetrated into many different areas, such as information communication, mathematics, physics, biology, computer science, even social science, and so on. It has become an extremely important scientific challenge topic. Related researches of the complex network mainly focus on three aspects. First is the establishment of complex network models. The second is the study on structural properties of complex networks. The last is the study on dynamics of networks, in which, chaos synchronization of complex networks has become a core and hotspot problem for its forward-looking theory and practical application, and it’s also the most concentrated direction in network dynamics research.Parameter identification and spatiotemporal chaos synchronization of complex network are studied in the dissertation. The main aspects are as follows:1. A method of parameter identification and synchronization of unidirectional star-network constructed by undetermined discrete spatiotemporal chaos systems is studied. The function to be determined in the parameter recognition law and the range of adjusting parameter are obtained based on Lyapunov theorem. Meanwhile, not only global synchronization of the network is realized, but also the unknown parameters in spatiotemporal chaos systems at the nodes of the network are identified.2. The control law used in controlling a linear discrete time system, designed by Milosavljevic, is extended and applied to synchronization and parameter identification of networks constructed by discrete spatiotemporal chaos systems with unknown parameters. The parameter identifier is designed by the extended control law. The unknown parameters in the spatiotemporal chaos systems at the nodes of the globally coupled network are effectively identified, and the global synchronization of the network is completed. The advantage of the method is that the parameter identifier designed by using the extended controlling law can be constructed only by the signal of the state variable in a single node before the network is connected, which greatly facilitates the theoretical design and practical application.3. Parameter identification and synchronization of complex dynamical networks constructed by continuous spatiotemporal chaos systems (partial differential equations) with unknown parameters are studied. The state variables in the systems with uncertain parameters are used to construct the parameter recognizers, and the unknown parameters are identified. Continuous spatiotemporal chaos systems are taken as the nodes of complex dynamical networks, and connection among the nodes is of nonlinear coupling. The structure of the coupling functions between the connected nodes and the control gain are obtained based on Lyapunov theorem. It’s seen that stable chaos synchronization exists in the whole network when the control gain is in a certain range.4. A method of realizing generalized chaos synchronization of a weighted complex network with different nodes is proposed. Chaos systems with diverse structures are taken as the nodes of the complex dynamical network. The nonlinear terms of the systems are taken as coupling functions, and the relations between the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov theorem. The research results show that generalized chaos synchronization can be realized in the whole weighted complex network with different nodes, even the coupling strength between the nodes is given any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength between the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network. This method is applicable to networks with both temporal and spatiotemporal chaos systems as nodes of complex network.5. The capability of the network synchronization under bounded noise is studied. The variation equations near the synchronization state is achieved based on stability analysis of the network, and the condition to realize spatiotemporal synchronization of the network is obtained through the standard transformation of Jordan. The synchronizing function of the network is further studied according to the change of the maximum Lyapunov exponent when bounded noise exists, and it’s found to have better capability of anti-jamming.6. A method to eliminate spiral waves and spatiotemporal chaos by synchronization transmission technology of network signal is proposed. The network error evolution equation with spatiotemporal variable and the corresponding eigenvalue equation are determined based on stability theory, and the global synchronization condition is further obtained. The research results show that any type of given external signal is input to any node in the network, all nodes in the network are synchronized to the external signal when the network achieves synchronization. That is, the given external signal has got synchronization transmission. The spiral waves and spatiotemporal chaos in the multiple systems can be suppressed effectively. |
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