Successive Projective Synchronization On A Class Of Complex Dynamical Network

Projective synchronization is a very important chaotic synchronization pattern.Projective synchronization is very common in real life,such as synchronous flight of aircraft formation,positioning of rocket,secure communications,etc.Therefore,studying the projective synchronization problem has important theoretical significance and practical value.However,there are still three problems in the research of projective synchronization on complex networks.First of all,the scale factor is uniform in the previous studies of projective synchronization.For the realization of network projective synchronization,this condition is too harsh.Secondly,in order to achieve projective synchronization under a given scale factor,it often needs to adopt strong nonlinear control,and needs to control most nodes of the network,even all nodes.From the perspective of practical application,the cost of control is too high.Finally,the existing communication security schemes designed by using the projective synchronization are only suitable for one-to-one transmission of information.If the sender wants to send a message to multiple recipients at the same time,the existing secure communication systems are not feasible.In order to solve the above problems,this thesis focuses on the following work:(1)In order to achieve successive projective synchronization with non-uniform scale factor,this thesis constructs a driver-response network model with distributed coupling.(2)In order to promote the successive projective synchronization of the dynamical network,the linear feedback controller,adaptive controller and impulsive controller are designed respectively to control the successive projective synchronization to the desired state.By using the Lyapunov function method,the global stability conditions of successive projective synchronization are obtained.The results show that if the coupling strength is large enough,then only controlling a node in the response network can realize the successive projective synchronization.Otherwise,multiple nodes need to be controlled.(3)Based on the successive projective synchronization theory,a secure communication system for one-to-many real-time information transmission is designed.(4)Numerical simulations are carried out by using the Matlab,which verifies the accuracy of the projective synchronization theory and the reliability of the secure communication system.The results in this thesis provide theoretical basis for chaotic secure communication on the network,and enrich the research content of network synchronization.