Discharge Pattern Analysis And Circuit Implementation Of A Memristor-based Morris-Lecar Neuron Model

Modifying neurons model according to the real biophysical environment helps analyze the mechanism of dynamic activity,improving the human cognition on brain activity,and giving the correct neuron information coding in application.Morris-Lecar(M-L)is a representative neuron model based on ion channel,but it does not consider the effect of electromagnetic induction.The complex transmembrane movement of ions in real neurons generates the time-varying electromagnetic field that can affect the membrane potential.Memristor can be used to simulate the coupling between membrane potential and electromagnetic induction in neuron equivalent circuit.In this thesis,memristor devices representing the relationship between magnetic flux and charge are selected to describe the electromagnetic induction phenomenon on the cell membrane,so as to improve the M-L neuron model and make it more in line with the physiological environment of human neurons.This thesis focuses on how neurons respond to the external stimuli and the biophysical mechanism of corresponding action potentials under different dynamic thresholds,and determines the energy efficiency of each ion channel.The switching trend of neuron firing patterns from the perspective of ISI is studied.It is confirmed that the different intensities of electromagnetic fields can produce different pattern transition in electrical activities of the neuron.Finally,a practical circuit that can reproduce the biological characteristics of neurons is designed using Multisim,which helps to understand the dynamics of a single neuron.The main research contents include:(1)The relationship between synapse and memristor is discussed in detail.It is rationalized that the memristor simulates the coupling part of neuron membrane potential and time-varying magnetic field.A three-dimensional M-L neuron model with electromagnetic induction is proposed.Based on the neuron equivalent circuit and spike threshold,the effect of the outward potassium channel on the spike threshold is analyzed.The influence of spike dynamic threshold on the input-output relationship of neurons is further analyzed.The energy function involved in the dynamics of neuron model with electromagnetic induction is derived,and the energy efficiency under different thresholds was determined.It is proved that the energy consumed by maintaining the time-varying magnetic field is a part of the energy required for different ions crossing the cell membrane.The biological significance of neuron firing pattern is explained by the energy consumption efficiency of different ion channels.(2)This paper proposes a new 4-D memristive M-L neuron model with threshold electromagnetic induction by using memristor to describe the interaction between membrane potential and time-varying magnetic field,which is closer to the real biological and physical environment.The trends of neuron firing pattern transitions under different parameters and parameter planes like the electromagnetic induction strength,the membrane capacitance and scale factor,et al.are explored.Applying the ISIs periodic number,the variance and the bifurcation in the multi-parameter planes and other methods,the trend of the neuron firing pattern transition is studied.The double parameter planes include membrane potential and capacitance,and time scale factor and magnetic field.It also confirmed that different intensities of electromagnetic fields can produce distinct pattern transition in electrical activities of the neuron.(3)Based on the 4-D nonlinear differential equation of the m M-L neuron model and applying the Multisim simulating circuit platform,the practical neuron model is designed.The design of the circuit unit of the hyperbolic tangent function and hyperbolic cosine function is solved.The whole circuit consists of capacitor,resistor,bipolar junction transistor,high precision operational amplifier and analog multiplier The circuit simulates the biological characteristics of neurons in the m M-L neuron model without simplification,resulting in the ability to reproduce spiking or bursting under different conditions,which provides a clear understanding of the neuron's firing switching mechanism.