Study On Stability And Applications For Discrete-time Neural Networks With Time-delays

In recent years,with the development of fractional-order calculus theory,fractional-order neural networks have been widely used in various fields,such as pattern recognition,associative memory,signal processing,and secure communication.Using the neural network model,we can realize the face recognition function.Then it can be further applied to many industries such as public safety,education services,medical services,business services,financial services,etc.,so as to provide relevant enterprises and departments with technical support in personnel management and achieve rapid and efficient development of enterprises.In these applications,the first issue is to analyze the stability of the network.At present,the research of fractional-order neural network is limited to continuous-time system.As is known to all,almost all numerical simulation results are obtained through continuous-time system discretization in computer simulation and simulation.Therefore,discrete-time fractional-order neural networks have attracted widespread attention from scholars at home and abroad.This paper investigates the problems of global Mittag-Leffler stability of fractional-order neural networks,existence and finite-time stability of discrete fractional-order complex neural networks with time delay,global Mittag-Leffler stability and synchronization of discrete fractional-order complex neural networks with time delay,and application of discrete-time quaternion-valued neural networks in face recognition.The details are as follows:(1)Global Mittag-Leffler stability of discrete-time fractional-order real-valued neural networksThis paper investigates the global Mittag-Leffler stability for discrete-time fractional-order real-valued neural networks.Based on the discrete fractional calculus theory and neural networks theory,a class of discrete fractional-order real-valued neural networks is proposed.By using inequality techniques and discrete Laplace transforms and constructing the appropriate Lyapunov function,the sufficient criteria of global Mittag-Leffler stability for discrete-time fractional-order real-valued neural networks are obtained.Finally,a numerical simulation example is given to verify the validity of the obtained results.(2)Existence and finite-time stability of discrete-time fractional-order complex-valued neural networks with time delaysWithout decomposing complex-valued systems into real-valued systems,the existence and finite-time stability for discrete-time fractional-order complex-valued neural networks with time delays are discussed in this paper.First of all,a new discrete Caputo fractional difference equation is proposed in complex field based on the theory of discrete fractional calculus.Additionally,by utilizing Arzela-Ascoli's theorem,inequality scaling skills and fixed point theorem,some sufficient criteria of delay-dependent are deduced to ensure the existence and finite-time stability of solutions for proposed networks.Furthermore,we have drawn the following facts: with the lower order,the discrete fractional-order complex-valued neural networks will achieve the finite-time stability more easily.Finally,the validity and feasibility of the derived theoretical results are indicated by two numerical examples with simulations.(3)Global Mittag-Leffler stability and synchronization of discrete-time fractional-order complex-valued neural networks with time delayWithout decomposing complex-valued systems into real-valued systems,this paper investigates the existence,uniqueness,global Mittag-Leffler stability and synchronization of discrete-time fractional-order complex-valued neural networks with time delay.Firstly,inspired by Lyapunov's direct method on continuous-time systems,a class of Lyapunov's direct method for discrete-time Caputo fractional-order complex-valued neural networks is further discussed.Additionally,based on the theory of discrete fractional calculus,discrete Laplace transform,discrete Mittag-Leffler functions,the theory of complex functions and Lyapunov's direct method,several sufficient conditions are established for global Mittag-Leffler stability and synchronization of the proposed networks.Finally,two numerical examples are also presented to manifest the feasibility and validity of the obtained results.(4)Application of discrete-time quaternion neural networks in face recognitionThis paper presents an associative memory face recognition algorithm for a discrete-time quaternion-valued neural networks model.The parameters of the proposed network are calculated directly by using the stability theory and singular value decomposition method of matrix.Then it can ensure that the equilibrium points of the network correspond to the face information that needs to be remembered.Numerical simulation results show that the constructed discrete-time quaternion-valued neural networks can recognize faces accurately.Therefore,it is beneficial for enterprises or management departments to conduct face management.