Nonlinear Dynamics And Stabilization Of A Class Of Fractional Memristive Neural Networks With Time Delay

The advantage of fractional-order calculus over integer-order calculus is that it can better describe the memory and genetic characteristics of materials and processes.Memristor is a non-volatile element,which can better simulate the synapses in human brain compared with the resistance.The existing research shows that a real capacitor is usually with fractional order in practical circuits.If applying the fractional-order capacitor to the large-scale circuit implementation of memristive neural network,a model of fractional-order memristive neural network(FMNN)is constructed.FMNN can describe the dynamical behaviors of human brain more accurately.Therefore,the study on dynamics and stabilization of FMNNs has important theoretical significance and practical application value.In this thesis,a class of FMNN with discontinuous memductance is proposed.The complex nonlinear dynamics of the model is studied by using numerical simulations.Then,the FMNN is stabilized by designing appropriate control laws.The main contents of this thesis consist of the following five chapters:In Chapter 1,the background and significance of memristive neural networks are introduced.The research status of nonlinear dynamics and stabilization of memristive neural networks is presented,and the main contents of this thesis is introduced.In Chapter 2,the definition of fractional derivative,the numerical solution method for fractional differential equations,and the stability analysis method of fractional systems are presented.The judging methods for chaos is given.In Chapter 3,a three-dimensional FMNN model is established.By using numerical methods,such as phase portraits,Poincare sections and bifurcation diagrams,the nonlinear dynamics of the model is analyzed.In addition,taking the initial value,the fractional-order and the switching jump as bifurcation parameter,respectively,the bifurcation of the above model is analyzed in details.The numerical simulation results show that unlike periodic doubling bifurcation,the route to chaos for the constructed three-dimensional FMNN is intermittent chaos.In Chapter 4,the stabilization of delayed FMNN is studied by means of fractional differential inclusion and set-valued mapping.A state feedback control law and a delayed state feedback control law are designed to achieve the globally asymptotical stabilization.Based on the stability of fractional-order linear systems and the fractional-order comparison principle,some stabilization criteria for delayed FMNN are proposed.The numerical simulation results show the effectiveness of the designed controller and the correctness of the proposed stabilization criteria.In Chapter 5,the main contents are summarized and the future work is presented.