Stability Analysis Of Two Types Of Memristive Neural Networks

As one of the most important algorithms in brain-like research,memristive neural network has attracted the attention of many scholars at home and abroad.Stability is one of the most basic dynamic behaviors of memristive neural networks,and its theoretical re-search involves the theory of differential equations,Lyapunov stability theory,impulsive control theory,biological science,computer science and other disciplines.The stabil-ity related achievements of memristive neural network have been widely used in pattern recognition,speech synthesis,associative memory and other practical projects.It is well known that memristive neural networks with impulsive control,fixed delay,time-varying delay,mixed delays,input saturation and other factors are relatively common models of memristive neural networks,and its stability is also a hot topic of research by scholars.Therefore,this thesis mainly studied the stability of two kinds of memristive neural net-works,including the following four aspects:the multi-valued linear piecewise memristor model,the stability of the multi-valued linear piecewise memristive neural network,the existence of the equilibrium point of the impulsive complex-valued memristive neural network,and the stability of the impulsive complex-valued memristive neural network.The main contributions and innovations of this thesis were as follows:(1)The stability of a class of piecewise linear memristive neural network was stud-ied.The model not only considered a multi-valued piecewise linear memristor model,but also considered the influence of external disturbance and time-varying delay on the system.In this thesis,the general piecewise linear model of binary memristor was intro-duced,and then a piecewise linear model of four-value memristor was given.Then,the stability criterion of the memristive neural network was obtained by using the comparison principle and Lyapunov stability theory.Finally,the validity of the results was verified by numerical simulation.(2)The stability problem of a class of complex-valued memristive neural networks with impulsive inputs was studied.The effects of impulsive input and mixed time delays on complex-valued memristive neural network were considered.Firstly,the complex-valued neural network was divided into two real-valued memristive neural network with real part and imaginary part,and then the two memristive neural networks were discussed at non-impulse time and impulse time respectively.The existence of the equilibrium point and the exponential stability criterion of the system were obtained by using squeeze crite-rion,Lyapunov function and inequality technique.Finally,the validity of the results was verified by numerical simulation.