Research On The Synchronization For Several Kinds Of Complex Networks

In the modern society,we are living in a variety of complex networks which are consisted of many individuals and the intricate connection between individuals,such as social networks,Taobao shopping networks,etc.The complex networks have been widely used in natural science and engineering field,and they have attracted many scholars of the complex network research upsurge.In particular,the synchronization control of complex networks has become one of the research hotspot in the control industry of scholars,and we have achieved rich achievements about it.But in the study of synchronous control of complex networks,scholars often assume that there are many constraints on the dynamic behavior of nodes and the topology of the network.However,the node dynamics and the topology in the real network are more complex.Therefore,it is still necessary to further study the problems of establishing a mathematical model closer to the real network and more effective design of the synchronous control method.Thus,in order to get closer to the real network,based on the existing research results,we established several complex network models,which are noise coupled nonlinear coupling,complex networks with switched topology,and memristor neural networks.Then,we designed many effective control methods such as adaptive control,intermittent control and event trigger control to study the quasi synchronization,asymptotical synchronization and finite time synchronization of the built models.The main contents and innovations are as follows:1.We study the quasi synchronization of a class of complex networks with time delay and noise interference.Because each node in the real network can not get the information of the neighbor nodes directly,it can only obtain the indirect information of the neighbor nodes.To this end,we first propose a mathematical model of nonlinear coupling complex networks with delay and noise interference.Secondly,in order to reduce the economic cost,we design a periodic intermittent controller which only need to pin a small number of nodes in the network,but not to control all nodes.Finally,we abtain some sufficient conditions for the quasi synchronization of the complex networks.2.We study the synchronization of a class of complex networks with non periodic switching of topological structures.For the real networks,the connection between nodes may lose or increase as time evolves,which results in the change of network topology.Therefore,we first established a network model with switch topology.Then,we design a aperiodic intermittent controller.When the switching topology contains a spanning tree,we only pin the zero-in-degree nodes;while the switching topology does not contain a spanning tree,we need not control any nodes.By constructing a multiple Lyapunov function and using the theory of M matrix,we propose some sufficient conditions for coupling strength and switching time to achieve global synchronization.3.We study the global exponential synchronization of a class of complex networks under the event triggered control strategies.To reduce the number of messages between nodes,we design two kinds of event trigger controllers which only need the nearest observation values of the neighbor nodes and the virtual leader,that is,the coupling information is updated only when triggering conditions are violated.Hence,the number of information transmission under the event triggered control is much less than that of the continuous control.Moreover,we also prove that the adjacent trigger time interval has a positive lower bound,which eliminates the occurrence of Zeno's behavior.4.We study the asymptotic synchronization of a class of random memristor neural networks with noise interference.In the process of transmission,information is unavoidable to be disturbed by noise and delay in time.A new state feedback controller and an adaptive controller are designed for a random memristor neural network with noise and time-varying delay.Based on set-valued mapping and differential inclusion theory,a suitable Lyapunov function is constructed.Then,by using Ito's formula and some inequality techniques,we obtain some sufficient conditions for the global asymptotical synchronization of random memristor neural network.5.We study the finite time synchronization of a kind of memristor neural networks with time-varying delay.In many practical applications,we always hope that synchronization can be realized in the finite time,and the speed of convergence is very high.We design a new type of controller with a switching parameter ?.Furthermore,the relationship between the selection of parameter ? and the initial value of error is discussed,and the influence of parameter ? selection on the synchronization time is discussed in detail.A sufficient condition for the memristor neural network to achieve the shortest finite time synchronization is put forward.