Modeling And Application Of Locally Active Memristor Devices

Locally-active memristor（LAM）can amplify weak signals.It has the advantages of nano-scale,memory,and low power consumption.It is an excellent device for building oscillators and artificial neural networks.At present,the theoretical analysis of LAM is mostly limited to a specific single model and lacks a general analysis method.Therefore,this paper carries out the quantitative theoretical analysis for general LAMs.We obtain the general law and universal design method for general LAMs and their oscillators.On this basis,a simplified modeling method of LAM is proposed,the LAM-based neuron circuit is designed,and a memristive neural network is constructed for pattern recognition.The main innovative work of this paper is summarized as follows:（1）Based on the small signal analysis method,local activity and Hopf bifurcation theory,a general analysis method for general LAMs is proposed.The important influence laws of three important physical parameters on the memristor and its oscillating circuit are revealed.It includes the quantitative relationships between the small signal admittance（impedance）function,the oscillating circuit frequency,and the external dynamic element parameter and the three physical parameters.To verify the above theoretical analysis,three different mathematical models of the LAMs are proposed.Although the three mathematical models are different,their three important physical parameters are identical.The simulation results show that the three different memristors show highly similar electrical behaviors,which verifies the correctness of the theoretical analysis.（2）Based on the experimental data of Nb Ox-based locally active memristor devices provided by Professor Robert Glen Elliman’s team from the Department of Electronic Materials Engineering,Australian National University,a simplified modeling method is proposed.The static voltage and current（DC V-I）curve of the Nb Ox LAM device can be roughly divided into three parts:high resistance region,negative differential resistance region,and low resistance region.The DC V-I relationship of the memristor is approximated by piecewise linear method,and a mathematical model is further established based on its dynamic behavior.Taking the physical model as an example,DC V-I curve is further subdivided into four sections,namely three inflection points.The simulation results show that the modeling method is effective.Then,an improved five-segment model is used to study the actual nano-device.The experimental results show that the model can accurately fit the static characteristics and dynamic behavior of the memristor.（3）Based on the LAM,the second-order and third-order neuron circuits are designed,respectively.The influence of important physical parameters on the spike firing behavior of the neuron is revealed.Under different input voltages and circuit parameters,a variety of neuromorphic behaviors generated by neuronal circuits are explored.Various neuromorphic behaviors of the proposed neuronal circuits are studied under different input voltages and circuit parameters.The simulation results show that both second-order and third-order neuronal circuits can emit spiking signals.The third-order neuronal circuit has more abundant neuromorphic dynamic behaviors,including chaotic behavior,refractory period behavior,and peak latency behavior.（4）By using the Nb₂O₅ memristor as neuron and the voltage-controlled memristor as synapse,a full-circuit neural network is established for pattern recognition.According to the proposed unsupervised learning method,synaptic weights are updated throughout the process.Only the synaptic weights of the most stimulated neuron conform to the input pattern.Taking the three 5×3pixel binary images as an example for recognition,the simulation results show that the circuit can correctly identify different patterns,which verifies the effectiveness of the proposed method.