Dynamics Study Of Memristor Neuron Circuits

Memristor is a new type of nonlinear electronic component with memory function.It has the characteristics of nanometer level and adjustable resistance value.In recent years,memristors have shown great potential in the field of neuromorphic computing,and Hodgkin-Huxley(HH)neuronal circuits have shown great promise in biomimetics based memristor.In order to reduce the complexity and energy consumption of neuronal circuits,a novel nanoscale third-order neuromorphic device has been developed,A single device can simulate multiple neuromorphic behaviors.In order to further study the circuit of memristive neurons and its application,it is necessary to propose a simplified mathematical model of memristor and reveal the mechanism of neural behavior.In this paper,a simplified mathematical model of memristor is constructed by piecewise linear method,which accurately fits the electrical behavior of Nb O_xlocally-active memristor(LAM).Based on this model,we studied the action potential fire mechanism of HH neuronal circuit and the dynamic behavior of third-order neuromorphic element in different working regions.The main innovative work of this paper is as follows:(1)HH neuron circuit is constructed based on piecewise linearized Nb O_xLAM memristor.By studying the change rules of neuron output signal with the model parameters of memristor and capacitance values,the firing conditions for generating action potential of the circuit are obtained.The simulation results show that the generation of action potential is closely related to the static electrical characteristics of the memristor.The circuit can simulate six kinds of neuromorphic behaviors,such as all or no,refractory period and periodic spiking,which verifies the correctness and effectiveness of the model.(2)A second-order oscillator circuit was constructed based on a single box-shaped resistor.The dynamic behavior of the oscillator circuit was quantitatively analyzed by the coordinate system shifting method and dynamic route analysis method,and verified by LTspice simulation software.The results show that the direction of the box-shaped hysteresis region has an important effect on the neuromorphic behavior of the oscillating circuit.The oscillating behavior of the box-shaped resistor in the clockwise direction has no resting state,and the box-shaped resistor in the anticlockwise direction can be used to generate the action potential.(3)Combining the box-shaped resistor model with the piecewise linearized LAM model,a simplified mathematical model of third-order neurons are proposed.The influence of initial state,capacitance,and memristor quasi-DC V-I curve on neural behavior fire were studied by numerical analysis method.The simulation results show that the proposed third-order mathematical model can simulate neuromorphic behaviors such as periodic spiking and periodic bursting.The locally-active theory proposed by Chua explains the dynamic behavior of memristor bias in the negative differential resistance region,and the above research work adds to the generation mechanism of the dynamic behavior of memristor bias in the box-shaped region and the positive differential resistance region.