Stability And Synchronization Analysis Of Complex-Valued Neural Networks

In the past decade,the research of complex-valued neural networks is increasing,and it has more superior characteristics than real-valued neural networks in complex signal processing.The state variables,activation functions and connection weights of complex-valued systems are defined in the complex domains.Processes and methods are greatly different from real-valued systems,so it makes sense to study complex-valued neural networks.This thesis mainly studies complex-valued system and two different neural network models are established.It uses Lyapunov function theory,Gronwall-Bellman lemma,complex function theory and inequality technology to analyze the specific system and obtain relevant theoretical criteria.The main works of this thesis are as follows:The global exponential stability of complex-valued neural networks with generalized piecewise constant arguments is analyzed.It has the characteristics of delay and advance.By choosing the appropriate Lyapunov function and skillfully combining inequality techniques,generalized piecewise constant arguments have been extended to the complex domains.The existence and uniqueness of solution are discussed.Some sufficient conditions to guarantee the global exponential stability of the system are obtained.The projection synchronization of complex-valued neural networks with generalized piecewise constant arguments has been discussed.The criterion of systems driven-response projection synchronization is obtained with linear control strategy and inequality technique,and it improves the existing results of synchronization analysis of complex-valued systems which have been obtained yet.We discuss a delayed memristive neural network model.According to the characteristics of memristive weights,based on differential inclusion theory to define the solution under the Filippov meaning and through adaptive control strategy to realize the adaptive synchronization result of systems to research on existing results expansively.This thesis studies the complex-valued system,the global exponential stability of the system and different types of synchronization behaviors are investigated.Some different theoretical techniques and criteria have been obtained by different techniques,and which provide a theoretical basis for further exploration of complex-valued systems.