Dynamical Analysis Of Delayed Inertia And Memristive Neural Networks

Artificial neural network is a kind of mathematical model which imitates the structure and function of biological neural network.It is mainly used to estimate and approximate the function,and has been widely used in combination optimization,pattern recognition,signal processing,secure communication and other fields.As two kinds of special neural networks,inertial neural networks can better describe the characteristics of biological neural networks,while the potential application of memristive neural networks in the next generation of human brain computer,so they have attracted many scholars' attention in recent years.This paper mainly analyzes the stability and synchronization control of inertial neural networks with mixed delays,as well as the dissipativity and synchronization control of fractional-order memristive neural networks with reaction-diffusion terms.The main works are as follows:1.The stability and synchronization control of the inertial neural networks with both time-varying delay and coupling delay are analyzed.By using the generalized nonlinear measure method,it is proved that the original system has a unique equilibrium point,and by defining an appropriate Lyapunov functional,a sufficient criterion for the global asymptotic stability of the equilibrium point is given.In addition,in the case of parameter mismatch,according to the matrix measure method,the quasisynchronization control of the master-slave systems is realized by designing a proper feedback controller.2.The dissipativity analysis and synchronization control of fractional memristive neural networks with reaction-diffusion terms are studied.By using fractional Halanay inequality and Wirtinger inequality,some sufficient conditions to ensure the global dissipativity of the system are given.Then,by designing appropriate controller,the sufficient criterion to ensure the exponential synchronization of the master-slave systems is derived,which is easy to verify.Some numerical examples are given to illustrate the effectiveness and correctness of the obtained results.