Research On Dynamics Of Memristor-based Neural Networks

A synapse of neuron simulation requires dozens of transistors,resistors capacitors in artificial neural networks(ANNs)circuits.Facing the incomparably complex human brain,traditional electronic components are powerless under the constraints of power consumption and size.As a new type of information storage and processing device,memristor has the characteristics of nanoscale size,fast switching and low power consumption.Its information storage and processing characteristics are very similar to the human brain synapse.Therefore,the ANNs based on memristor,that is,memristor-based neural networks(MNNs),have gradually become the research focus in the fields of artificial intelligence,information processing,nonlinear networks and so on.In the application of MNNs,we always expect MNNs to have good performances of global stability and synchronization.However,under the action of noises and information transmission delays,MNNs show complex nonlinear dynamic phenomena.Therefore,it is an important work to study the dynamic behaviors of MNNs in theory and get a deep understanding.The dynamical behaviors of MNNs with time-varying delays are studied in this paper,including robust stabilization,dissipativity and passivity,pinning impulsive synchronization,input-to-state stability(ISS)and exponential synchronization.The contents of this research and main results are as follows:1.The problem of robust stabilization is addressed for MNNs with time-varying delays.Firstly,a class of coupled neural networks circuit is designed by using the properties of memristor and the structure of neuron,and the fuzzy model of MNNs is proposed.Secondly,based on T-S fuzzy theory and Lyapunov-Krasovskii functional(LKF)method,robust stabilization criteria are proposed in form of linear matrix inequalities(LMIs).Finally numerical examples are presented to demonstrate the effectiveness of the proposed robust stabilization criteria,which well support theoretical results.2.The problem of dissipativity and passivity is studied for MNNs with both timevarying leakage delay and two additive time-varying delays.By introducing an improved LKF with triple integral terms,and combining the reciprocally convex combination,Wirtinger-based integral inequality with free-weighting matrices,some less conservative delay-dependent dissipativity and passivity criteria are proposed.The proposed criteria that depend on the upper bounds of the leakage and additive time-varying delays are given in terms of LMIs,which can be solved by MATLAB LMI Control Toolbox.Finally,some examples are given to illustrate the effectiveness and superiority of the obtained results.3.The problem of exponential and asymptotical synchronization is discussed for stochastic memristor-based neural networks(SMNNs)with time-varying delays via pinning impulsive control.Based on the physical properties of memristor,the mathematical model of SMNNs is obtained by the theories of drive-response concept,set-valued maps and stochastic differential inclusions.Then some sufficient verifiable conditions are proposed for the synchronization of SMNNs by applying the LKF method and designing a novel type of pinning impulsive controllers.Finally,numerical examples are presented to demonstrate the effectiveness of the theoretical results.4.The problem of input-to-state stability is considered for discrete-time memristive neural networks(DMNNs)with two delay components,and the problem of exponential synchronization is studied for DMNNs with time-varying delays.A dynamic delay interval method is used to relax the restriction on upper and lower bounds of the DMNNs delay intervals,which extends the fixed interval of a time-varying delay to a dynamic one.First,a tractable model of DMNNs is obtained via using semidiscretization technique.Furthermore,by constructing several novel LKFs and using Refined Jensen-based inequalities,we propose some new sufficient conditions in the form of LMIs to ensure that the DMNNs with two delay components are input-to-state stable and the master and slave systems with time-varying delays are exponential synchronized.Finally,some numerical examples are presented to demonstrate the effectiveness of our theoretical results.