Intralayer Synchronization Of Multiplex Neural Networks Via Pinning Control

Most real-world complex networks are not single-layer,there are interconnections between the networks.The phenomenon of synchronization can be seen everywhere in real life.It is more actual to study the synchronization of multiplex networks than the synchronization of single-layer networks.As a type of complex networks,neural networks construct the information processing process in the real world by simulating the transfer characteristics of neural impulses between biological neurons.In recent years,neural network has played a significant role in many fields,such as pattern recognition,machine learning,signal processing.The synchronization of neural networks is also a hot topic studied by a large number of experts and scholars.Since the actual networks usually contain a large number of nodes and their topological structures are intricate,it is more economical to realize synchronization of multiplex networks via pinning control.However,the previous studies have focused on the pinning control of the single-layer neural networks,there is almost no research on the pinning synchronization of multiplex neural networks.In this thesis,based on the two-layer neural networks with undirected connections between layers,the problem of intralayer synchronization of multiplex neural networks via pinning control is studied.Main contents of this thesis are summarized as follows:1)The intralayer synchronization of multiplex integer-order neural networks is studied via pinning impulsive control.Different from previous studies,time-varying delay,distributed-delay and external disturbance are considered in the multiplex integer-order neural networks model in this thesis.Besides,an appropriate pinning impulsive control strategy is designed to realize intralayer synchronization of multiplex neural networks.Based on Lyapunov stability theory and impulsive control theory,this thesis deduces the intralayer synchronization criterion of multiplex integer-order neural networks,and estimates the least number of nodes that each layer needs to pin.Finally,a numerical simulation example demonstrates the correctness and effectiveness of the theoretical results.2)The intralayer synchronization of multiplex fractional-order neural networks is studied via pinning linear feedback control and pinning adaptive control,respectively.Timevarying delay is considered in the multiplex fractional-order neural networks model.Based on Lyapunov stability theory,this thesis derives the intralayer synchronization criterions of multiplex fractional-order neural networks via pinning linear feedback control and pinning adaptive control,respectively.Finally,numerical simulations verify the correctness and effectiveness of the theoretical results.