| Chaos synchronization,also known as chaos synchronization control,is a branch of chaos control.The difference between chaos synchronization and traditional chaos control is that the goal of chaos synchronization is to reconstruct two or more chaotic states completely,while the goal of traditional chaos control is to stabilize chaotic motion on an unstable periodic orbit.The theory of chaos synchronization has experienced a few decades development since it was put forward.At present,the theory of chaos synchronization has achieved fruitful research results,some of which have been successfully applied,such as secure communication,image encryption and UAV formation control.Nevertheless,chaos synchronization theory is still a research hotspot in the field of nonlinear science.The existing types of chaos synchronization mainly include complete synchronization,generalized synchronization,cluster synchronization and so on.Based on complete synchronization and cluster synchronization,the synchronization of partial state components in chaotic network system is studied in this paper.In real life,sometimes there are such synchronization control problems:(1)the ultimate goal of control is only the synchronization of part of the state components,not all of the state components;(2)because of the structural factors of the network system,it is impossible to achieve synchronization of all the state components,or the control technology needed to achieve synchronization of all the state components is more difficult;(3)the synchronization of all state components in network system will consume a lot of manpower,material resources and time,but the actual control effect is little different from that of part of the state components.At this time,synchronization of partial state components will be the best choice.Therefore,it is of great significance to study the synchronization of some state components in chaotic networks.Based on the above problems,a series of studies on the synchronization of partial state components in a class of chaotic network systems are carried out.The main work and innovations are as follows:(1)The sufficient conditions for synchronization of partial state components in a class of continuous chaotic network systems are studied.Firstly,the definition of synchronization of partial state components in continuous chaotic networks is proposed,that is,some state components of all nodes in the network converge asymptotically over time.Then,Lyapunov stability theory,matrix theory and graph theory are used for theoretical analysis and derivation.Under the global or local QUAD condition,the sufficient conditions for synchronization of partial components in a class of chaotic network systems has been derived,and correctness of the theoretical results is verified by numerical simulation with MATLAB software.The innovations are as follows: The concept of partial state component synchronization in continuous chaotic networks is proposed,and the sufficient conditions for partial state component synchronization in a class of conditions chaotic networks are deduced theoretically.(2)Sufficient conditions for synchronization of clustering state components in a class of disconnected continuous chaotic network systems under traction control are studied.Firstly,the definition of synchronization of clustering state components in unconnected continuous chaotic networks is proposed,that is,a part of the state components of all nodes within each cluster in the network converge asymptotically over time.Similarly,Lyapunov stability theory,matrix theory and graph theory are also used for theoretical analysis and derivation.For undirected network topology and directed network topology,several sufficient conditions for realizing clustering component synchronization of unconnected continuous chaotic network system under traction control are derived,and numerical simulation is carried out by using MATLAB software to verify the correctness of the theoretical results.The innovations are as follows: The concept of clustering component synchronization in unconnected continuous chaotic network system is proposed,and several sufficient conditions for realizing clustering component synchronization in a class of unconnected conditions chaotic network system under traction control are theoretically derived.(3)The sufficient conditions for synchronization of partial state components of a class of discrete chaotic network systems are studied.Firstly,the definition of partial state component synchronization in discrete chaotic networks is given.Then,the sufficient conditions for partial state component synchronization of two identical discrete chaotic systems under coupling conditions and the sufficient conditions for partial state component synchronization of symmetric chaotic networks composed of N identical discrete chaotic systems under traction control conditions are discussed,and the correctness of the theoretical results is verified by numerical simulation with MATLAB software.The innovations are as follows: The concept of partial state component synchronization in discrete chaotic networks is proposed,and several sufficient conditions for partial state component synchronization in discrete chaotic networks are deduced theoretically. |
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