Study On Synchronization And Multistability Of Delayed Memristive Neural Networks

Memristor which can imitate synapse because of its nonvolatility has been widely used in neural networks.Based on the good characteristics of memristor,new neural networks can be designed by using memristor to replace resistor in the circuit of traditional neural networks,namely memristive neural networks.Due to extensive application prospect in secure communication,image encryption and associative memory and so on,synchronization and multistability of memristive neural network have received increasing attention.In addition,different memristive neural network models have different application scenarios,for example,the inertial term of two-order memristive neural network is considered as a key factor to generate complicated bifurcation and chaos behavior.Because delays inevitably exist in some elements including amplifier used in the circuit of memristive neural network,more realistic delayed memristive neural network model and its dynamical behaviors have attracted increasing attention.This dissertation mainly studies synchronization and multistability of some types of delayed memristive neural networks.By using event-triggered control scheme,synchronization of inertial memristive neural networks is achieved.Robust synchronization and multistability of two types of delayed memristive neural networks with parameter perturbations are realized,respectively.Moreover,exponentially stable equilibrium points can be flexibly located in the even-sequence regions.In addition,two types of new synchronization modes are proposed to extend the existing synchronization modes.The specific contents and innovations can be summarized as follows:(1)Event-triggered synchronization mode of delayed inertial memristive neural networks(IMNNs)is proposed.According to two types of response system models,state feedback controllers are constructed and static and dynamic event-triggered control schemes are designed,then some sufficient conditions are given to ensure the synchronization of drive and response delayed inertial memristive neural networks.Finally,a numerical simulation and some data analyses are given to verify that event-triggered control schemes can effectively reduce the update frequency of controllers and decrease computational burden.(2)By introducing uncertain parameters and mismatched parameters,more realistic delayed memristive neural network model with two types of parameter perturbations is built and its robust multimode function synchronization mode is proposed.Then,two adaptive controllers including function r(t)and update gain?are designed to achieve robust multimode function synchronization of delayed memristive neural network with parameter perturbations.This synchronization mode can take multiple types of complete synchronization including power-rate synchronization and exponential synchronization as its special cases,and extend the existing synchronization modes.Finally,numerical simulations are put forward to explain that r(t)and?can control synchronization mode and speed,respectively,and verify the correctness and validity of theoretical results.(3)Delayed memristive Cohen-Grossberg neural network model with stochastic parameter perturbations is built.Utilizing fixed point theory and differential inequality,exponential multistability of the network model can be achieved.Moreover,exponentially stable equilibrium points can be flexibly located in the odd-sequence or the even-sequence regions,and there exist(w+2)~l(or(w+1)~l)exponentially stable equilibrium points in the odd-sequence(or the even-sequence)regions,this means that delayed memristive Cohen-Grossberg neural network with perturbations can be applied to some areas,such as associative memory storage and secure communication.Finally,two numerical examples are given to verify the correctness of the obtained results.(4)Delayed coupled memristive neural network model is built,and hybrid multisynchronization type of coupled memristive multistable neural networks with time delay is proposed.Some sufficient conditions are derived to guarantee that delayed coupled memristive neural network can acquire(r+2)~n stable equilibrium states.Then,using Lyapunov functional and linear matrix inequality methods,some sufficient conditions are given to achieve hybrid multisynchronization of coupled memristive neural networks with time delay under multiple stable equilibrium states.Compared with other multisynchronization types,hybrid multisynchronization is more flexible and practical,and extend the existing synchronization modes.Finally,numerical simulations are given to illustrate the superiority of hybrid multisynchronization.