| Rectent years, control and synchronization of nonlinear systems which consist of two or more nodes has been a hot toptic. It is a interesting work how to synchronize two chaotic systems. However, because of the complexity of chaos, this work is very difficult. On the other hand, in the real world, many systems are some huge networks which are composed of many subsystems. And the number of subsystems is much large than two. Evidentlly, it is worth to investigate how to synchronize the huge networks. In fact, the human society is a huge network itself. Along with the advance of technology, the communication of peoples is not only convenient more and more, but also wide more and more today. But, at the same time, this tight relationship of peoples also makes an opportunity for the lagre scale outbreak of epidemic. Thus, it is an important work how to control the epidemic effectively.Based on mentioned above, in the Ph.D. Dissertation, firtly, some basic concepts of chaos and complex network was introduced, include of the origin, developments and type methods of chaotic control and synchronization; and then, the investigation of how to improve the precision and speed of synchronization was described; the concept and method of rotating synchronization was proposed; the module-phase synchronization and lag synchronization of complex chaotic systems were realized. Further more, the synchronization of hybrid states on complex networks was also investigated. Finally, aimed at the shortcoming of existed immunity strategies, a new immunity strategy was desgined. The specific details of our work as following:(1) Through analysis the major factor of the effect of synchronization precision and speed, an optimal control matrix was designed. When the synchronization error increased, the control gains were also improved in time. A high precision fast projective synchronization was realized. Compare with the available methods in literature, the numerical simulations indicate that the synchronization precision was increased remarkably. At the same time, the iteration times was also sharply reduced. And, when e< 10-3, the iteration even need only once. Further more, when the system parameters were unknown, the high precision fast synchronization also was realized. And the theoretical ananlysis and proof were also given.(2) A chaotic synchronization on defferent azimuth-rotating synchronization was proposed. And its validity and feasibility were proved via theoretical analysis and numerical simulations. Three conclusions were obtained:firstly, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different azimuth can realize synchronization; secondly, projective synchronization is a special case of rotating synchronization, so, the application field of rotating synchronization is more wider than that of projective synchronization; thirdly, the overall evolving information can be reflected by single state variable’s evolving, this is the same as the basic idea of phase space reconstruction method, it indicates that our method and the phase space reconstruction method verifies each other.(3) The module-phase synchronization and lag synchronization on complex chaotic system were investigated respectively. The adaptive controllers were designed to synchronize the two complex chaotic systems with time delay. The results indicate that the method is effective. And then, aimed at the characteristics of complex system, the module-phase synchronization was investigated. The chaos synchronization between drive system and response system was realized in module space and phase space respectively (module-phase synchronization). Different from the evolutions in real space, there no pseudorandom behaviors in phase space when the module-phase synchronization was achieved. When the module-phase synchronization was achieved, all the phases of complex state variables were switched between two fixed values which decided by initial values of drive system. And the modules varied in a bounded field.(4) Chaotic synchronization of hybrid state on complex networks was investigated. In real application, the measurable physical quantities always are hybrid states instead of the states itself. From the point of view of practice, the chaotic synchronization of hybrid state on complex networks was investigated in this paper. Compared with general synchronization method, a new error dynamic system was constructed. And the controller which is determined by the error of hybrid states and hybrid matrix was designed. The theoretical analysis and proof were given, as well as numerical simulations. The results indicate that our method is effective and feasible.(5) Aimed at the shortcoming of existed immunity strategies, a new immunity strategy was desgined. We proposed an efficient immunization-"high-risk immunization". The standard SIRS model was modified respectively on WS small world network and BA scale free network. Based on our new SIRS model, the density of infected individuals was analyzed from a theoretical point of view, and computer simulation was implemented on different networks. The results indicate that the high-risk immunization is effective, and it is economic and feasible in practice. |
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