Dynamic Analysis And Control Of Fractional Order Memristor Neural Network

Neural network is a new interdisciplinary subject.It has unique knowledge representation structure and information processing principle,which provides new ideas for control problems and intelligent information processing.The neural network based on memristor is applicable to the new model and new data.If the memory resistor is used as the weight of the neural network circuit,the network computing,parallel and adaptive ability will be improved.The fractional derivative can provide the overall computing power for the neuron,which is more conducive to the information transmission of the neuron.The fractional order is introduced into the memristive neural network system and taken into account the memory of the neuron,so the application of neural network will be more widely applied.In recent years,the memristor neural network system with fractional order node dynamics has received extensive attention.Based on the existing research results,this thesis considers the stability,synchronization and control of neural networks under the influence of time delay and parameter mismatch.All the results are verified by numerical simulations.The work of this thesis is summarized as follows:1.An intermittent control scheme is adopted to deal with the synchronization problem of fractional-order memristive neural networks(FMNNs)with switching jumps mismatch.A fractional order differential inequality is introduced.Based on differential inclusions theory and the properties of Mittag Leffler function,some intermittent synchronization criteria are derived.The synchronization regain related to fractional order,control period and the control width is discussed in details.In addition,based on the results of fractional order stability and interval matrix inequalities,fractional order memristive delayed neural networks systems are transformed into interval parameters systems,aperiodically intermittent controllers are designed and general fractional order differential inequalities are obtained to synchronize the coupled systems.Sufficient conditions are obtained to guarantee quasi synchronization of the studied system.2.This section studies exponential stability of fractional order memristor discontinuous neural networks(FMDNNs).Under the framework Filippov solution,the global existence of the solution for the FMDNNs is obtained by given growth conditions.Based on the Lyapunov stability theory,some new criteria for the stabilization of FDNNs are obtained by using the effective partial state impulsive control,which only needs to control a small fraction of the states.At every impulsive moment,these states of the trajectory far away from the desired trajectory will be firstly controlled.Inaddition,we consider drive response exponential synchronization in fractional order memristive bidirectional associative memory(BAM)neural networks.Based on the theories of fractional calculus and the definition of average impulsive interval,several criteria for achieving synchronization of studied system are established under different impulsive effect.Fractional order has an influence on the impulsive effect and more extensive ranges of impulsive effects are considered.3.This section studies drive-response synchronization in fractional-order memristive neural networks in the case of switching jumps mismatch.A comparison theorem for fractional-order systems with fractional order ? ?(n-1,n)is provided first.Based on Laplace transform and linear feedback control,some lag quasi-synchronization conditions are obtained with variable order ? ?(0,1)and ? ?(1,2).In the R-L type fractional order system,through the use of Babalate lemma and stability theory,establishing inequalities,the projective synchronization criteria of the fractional memristor time varying delay system are obtained.4.This section studies synchronization in fractional order memristive Cohen-Grossberg neural networks.By applying the asymptotic expansion property of Mittag Leffler function and the definition of average impulsive,some sufficient conditions based on feedback control and impulsive control are established for achieving finite time synchronization and exponential synchronization of the considered systems.Moreover,the selection of impulsive gain depends on the fractional order ?.The upper bound of the setting time for synchronization is estimated and the precisely exponential convergence rate is obtained when two controllers are utilized.