The Synchronization Control For Several Class Of Directed Complex Networks With Reaction-Diffusion Term

Complex network refers to a network with some or all properties of self-organization,self similarity,attractor,small world and scale-free.Because it can help people un-derstand and study the essence of things better,complex network has attracted the attention of many scholars at home and abroad in recent years.As a representative of complex network,neural network has been successfully applied to pattern recognition,intelligent control and combinatorial optimization.Synchronization analysis and con-trol of coupled neural network composed of multiple neural networks are central topics in the investigation of complex network dynamics.In this paper,by combining complex network theory,cybernetics and Lyapunov stability theory,the synchronization control of directed coupled neural network and directed complex network is studied under the influences of reaction-diffusion,time-varying delay,external disturbance and stochastic noise.The main contents of this paper are summarized as follows:1.By utilizing four different kinds of intermittent boundary control,the complete synchronization of a directed coupled neural network is studied,which includes both reaction-diffusion term and mixed Dirichlet-Neumann boundary condition.Firstly,the exponentially complete synchronization of the network is realized by the intermittent boundary control with distributed measurement and spatial sampled-data measurement respectively.This method of intermittent control only on the boundary of the space can greatly improve the efficiency and reduce the cost of control.Secondly,the asymp-totically complete synchronization of the network is realized by the hybrid intermittent boundary control with constant gain and adaptive gain respectively.In this hybrid control,when the variable of state error on the boundary is not zero,we control the network on the boundary,and when the variable of state error on all boundaries is zero,that is,when the boundary control fails,we control the network within the space region.2.By utilizing a spatial sampling control,the H_?synchronization of a direct-ed coupled neural network is studied,which includes both reaction-diffusion term and mixed time delays.Firstly,the network model contains not only a mixed Dirichlet-Neumann boundary condition,but also some discrete and distributed time delays.Sec-ondly,the spatial sampling control only measures the value of the network state at certain fixed spatial sampling points,which can reduce the number of data updates on the spatial area of the controller.Finally,not only the effect of state coupling,but also the effect of spatial diffusion coupling on the synchronization is considered.It is found that state coupling promotes the synchronization of network,while spatial diffusion coupling inhibits the synchronization of network.3.By utilizing an event-triggered quantized control,the H_?output synchroniza-tion of a directed coupled neural network is studied,which includes reaction-diffusion term in high dimensional space.In the quantized control protocol based on event trig-ger,we first take time sampling for the state variables to avoid the occurrence of Zeno phenomenon,and then judge the trigger condition of the sampled data.If the condi-tion is satisfied and the event is triggered,the data is quantized and transmitted to the controller.In addition,the sufficient conditions to ensure the synchronization of the network are only related to the number of neurons in the network,but not to the number of nodes.This will be beneficial to the calculation and verification of these sufficient conditions.4.By utilizing the switched pinning control with constant gains,centralized adap-tive pinning control and distributed adaptive pinning control,the cluster synchroniza-tion of a directed complex network is studied.The considered network includes reaction-diffusion term,stochastic noise and Markovian switching.Firstly,for the target state of cluster synchronization,we choose the average state of the nodes in the same cluster,rather than a given isolated node.Secondly,we only require that the subgraphs made up of the nodes in the same cluster are strongly connected,while the subgraphs of the nodes in the different clusters can be unconnected.The main theoretical results of the above studies are verified by some numerical examples,using MATLAB software.