The Desynchronization Of The Multi-weight Coupled Neural Network Is Desynchronized With The Finite Time

In recent years,neural network has attracted more and more attention because of its wide applications in signal processing,optimization,associative memory and other fields.As a special complex network,coupled neural network is composed of several interactive neural networks.Therefore,the discussion of dynamic behaviors in coupled neural networks has become a hot topic.However,most of the existing works on coupled neural networks only considered single-weight network models.In fact,most network models in the real world are more accurately represented by multi-weighted complex dynamic networks,such as social networks,communication networks,transportation networks,etc.,which are coupled by nodes in the form of multiple coupling.Therefore,it is of great significance to study the multi-weighted coupled neural networks.In this paper,two multi-weighted coupled neural network models with and without time-varying delays are proposed respectively,and the anti-synchronization and finitetime anti-synchronization of the considered networks are studied by using Lyapunov stability theory and some inequality techniques.Firstly,the anti-synchronization problem of multi-weighted coupled neural networks is analyzed by constructing suitable Lyapunov functional and using some inequality techniques,and the anti-synchronization conditions of the network are given.At the same time,by designing appropriate pinning adaptive controller to control a part of nodes in the network,we further study the antisynchronization problem of the network,and obtain some effective criteria to ensure that the network achieves pinning anti-synchronization.Secondly,because the neural network is realized by electronic circuits,when electrons are transmitted in a non-uniform magnetic field,the reaction-diffusion phenomenon is inevitable.Therefore,a multiweighted coupled reaction-diffusion neural network model with reaction-diffusion term is proposed,and its anti-synchronization analysis and control are carried out.In addition,in many practical applications,it is usually necessary to achieve anti-synchronization within a limited time interval.Therefore,this paper further studies the finite-time antisynchronization problem of multi-weighted coupled neural networks.As we all know,time delay inevitably occurs in practical applications such as communication,information conversion and biological systems.In particular,there is usually a time delay during signal processing and transmission in most circuits.Therefore,we further consider the anti-synchronization and finite-time anti-synchronization of multi-weighted coupled neural networks with time-varying delays.Finally,we give several numerical simulation examples to prove the validity and correctness of the results.