Dynamical Analysis Of Complex-valued Time-delay Memristive Neural Networks

Since the invention of the first physical memristor device,it has attracted much attention because of its similar features as the neurons in the human brain.Different from the traditional neural networks,the memristor-based neural networks are a class of state-dependent non-linear switching systems,which is more flexible and practical.In addition,due to the nano-scale size,high storage capacity,and non-volatile characteristics of the memristor itself,it has a wide application prospects.Therefore,memristive neural network has become one of the research hotspots in recent years.Considering that dynamic analysis is the premise and foundation of neural network application,this paper considers the dissipative behavior of delay memristive neural network model,as well as the global exponential stability and synchronization control of complex-valued memristive neural network model.The main content of this thesis describes as follows:1.The(Q,S,R)-?-dissipative problem of delayed memristive neural networks is analyzed.By constructing an appropriate Lyapunov function,using the Bessel-Legendre inequality technology,the sufficient conditions to guarantee the dissipative property of the memristive neural network are given in the form of linear matrix inequality.The obtained result improves some existing one and reduce the system's conservative.2.The global exponential stability and sampled-data synchronization of delayed complex-valued memristive neural networks are studied without separating the system into real and imaginary parts.Based on the homeomorphism theory and Lyapunov function method,the sufficient conditions to guarantee the existence and global exponential stability of the unique equilibrium point for complex-valued system is given.Meanwhile,a sampled-data controller is designed to synchronize the master and slave systems under the framework of inequality techniques and Lyapunov method.The obtained results not only improve corresponding results in the previous and have less conservative,but also have a wide application.The numerical simulation verifies the correctness and validity of the obtained results.