Research On Synchronization Control Of Stochastic Complex Networks With Delay

Complex networks have developed rapidly since the 20 th century and have been widely used in biology,medicine,practical engineering and other fields.Complex networks are composed of nodes and connected edges.In addition to the inherent coupling,time delay is also common in complex networks.In addition,noise and other factors in the external environment will also affect the complex network.Synchronization,as a typical subject in the study of complex network dynamics,has been deeply concerned.Due to the influence of network complexity and external uncertain disturbance,in order to make the node states of the complex network system with stochastic time delay tend to the same trajectory,this paper reasonably uses various control methods and strategies to solve the synchronization problem.Specifically,the main contents of this paper are as follows:First,considering the external environment and actual situation,a stochastic complex network model with mixed time delay is established,and a controller based on adaptive aperiodic intermittent control strategy is constructed.The controller can ensure that the network system with parameter uncertainty or disturbance characteristics can achieve synchronization within a finitetime.In addition,based on various inequality techniques,a finite-time synchronization criterion is obtained by establishing a Lyapunov function.Moreover,synchronization can still be achieved when there is no random disturbance in the system.Finally,the rationality of the theoretical results is verified by a simulation example of Chua’s circuit system.And,the fixed-time synchronization problem of stochastic complex networks with mixed delays is further studied.A new intermittent controller is designed to make the system independent of the initial value and achieve synchronization in a certain time.The controller avoids the influence of symbol function and is also suitable for directed networks.The Lyapunov function is established,and the sufficient condition of fixed time synchronization is deduced.Then,a simulation example is used to verify the effectiveness of the proposed method.Finally,the synchronization control problem of stochastic complex networks with time delay is studied in depth.First,by selecting nodes of stochastic complex networks with large error norm,a new type of restraining impulse controller is constructed,which not only saves control resources,but also ensures that the complex networks with stochastic time delay can achieve finite-time synchronization.Secondly,based on the idea of average impulse interval,the unified finite-time synchronization criterion under synchronous impulse and desynchronized impulse is derived.The obtained effective conditions are further extended to general stochastic complex networks and stochastic delay complex networks with delay impulses.Finally,the feasibility of the theoretical results is verified by numerical examples.