The Promotion Of Complex Dynamic Networks Lag Synchronization And Lag H_∞ Synchronization

Recently,the dynamical behaviors of complex networks have been discussed widely.As one of the classical dynamical behaviors of complex networks,the synchronization exists universally in nature and society.Because of the wide applications of the synchronization of complex networks in different fields(secure communication,information processing,biological systems and other engineering sciences),the problem of the synchronization for complex networks has become a hot topic.However,most of the existing works on complex network only considered the network models with single-weight.In fact,most network models in the real world are more accurately described by multi-weighted complex dynamic networks,such as social networks,transportation networks,communication networks.Therefore,it is of great significance to study the multi-weighted complex networks.In addition,time delays often inevitable appear in practical applications,such as communication,information conversion and biological systems.For example,it is usual to expect that time delays exist during the processing and transmission of signals in most circuits.Therefore,we investigate the lag synchronization of multi-weighted complex networks in this paper.Moreover,as a special kind of complex networks,the synchronization of coupled neural networks has been widely discussed.Considering that the different diffusion of node could affect other nodes and in coupled neural networks,the coupled reaction-diffusion neural network model with state coupling and spatial diffusion coupling is studied in this paper,respectively,and the problem of the lagH_∞synchronization for proposed network models is investigated by using the Lyapunov functional method,some inequality techniques and designed controllers.Firstly,the lagH_∞synchronization problem of the coupled reaction-diffusion neural network is analyzed by constructing suitable Lyapunov functional and using designed state feedback controller and adaptive feedback controller,and several lagH_∞synchronization criteria for the considered network are given.Secondly,because the neural network is realized by electronic circuit,the reaction diffusion phenomenon is inevitable once the electrons transport in inhomogeneous magnetic field.Therefore,a coupled reaction-diffusion neural network model with spatial reaction-diffusion coupling is proposed,and the analysis and adaptive control of the lagH_∞synchronization for the proposed network is carried out.Finally,several numerical simulation examples are presented to prove the validity and correctness of the results.