| The nonlinear dynamic behavior of neurons in information coding and discharge activities is very complex.It is impossible to explain the experimental phenomena using the statistical method and the linear thinking.Applying the theory and method of nonlinear dynamics is helpful to study the neural system information conduction process and coupling mechanism,and reveal how the parameter changes of the neural model and the external stimuli impact on the neurodynamic behavior.It can not only provide ideas for biological neural experiments,but also help to reveal the storage and coding mechanism of the brain.In this thesis,the Hindmarsh-Rose neuron is used as the object of study,and based on magnetic field the coupling phenomenon between neurons is studied.The HR neuron mathematical model with coupling magnetic field based on memristor is built.The dynamic characteristics of the magnetic field coupled neuron model are analyzed in detail on the basis of numerical calculation.The Hamiltonian energy function of the system is derived to study the conversion mechanism of neuron discharge mode from the energy point of view.Multisim circuit simulation software is used to design a practical circuit that can reproduce the biological characteristics of neurons,which is helpful to understand the mechanism of neuron firing switch.The main research contents include:(1)The relationship between synapses and memristors of biological neurons is analyzed in detail,and the rationality of memristors simulating the coupling of adjacent neurons through time-varying magnetic field is discussed.The time-varying selffeedback magnetic field and coupled magnetic field in neuron environment are simulated with an improved threshold magnetically controlled memristor,and a timedelayed coupled double-HR neural network model with memristor electromagnetic coupling term is proposed.The effect of coupled magnetic field on the dynamic behavior of the model is analyzed by single-parameter bifurcation diagram,twoparameter bifurcation diagram,time series diagram and phase plane diagram.It is proved that the coupling magnetic field can activate resting neurons to produce abundant discharge patterns,such as spike discharge,cluster discharge,chaotic discharge,and magnetic field makes the amplitude and rhythm of neuron discharge change regularly.(2)The relationship between the time delay and the discharge mode in the coupling process is studied.The results show that a proper time delay can make the neurons more responsive to external stimuli and coupled magnetic fields,and keep the neurons firing periodically under a wider range of external excitation currents.Based on Helmholtz theorem,the general form of generalized Hamilton energy function is derived,and applied to magnetically coupled neuronal systems.The effects of magnetic field and time delay on discharge mode are explained from the perspective of energy,and the corresponding relationship between energy function and membrane potential is analyzed.(3)Based on the 6-D nonlinear differential equation of memristor magnetically coupled neurons,the bi-hyperbolic tangent function memristor circuit and the practical circuit of memristor magnetically coupled neurons are designed by using Multisim analog circuit simulation platform.The whole circuit consists of capacitor,resistor,bipolar junction transistor,high precision operational amplifier and analog multiplier are selected.The biological characteristics of neurons are simulated without simplification,and the peak discharge and cluster discharge under different magnetic fields are reproduced.The results coincide with the simulation result using Matlab,which is helpful to understand the firing switching mechanism of neurons. |
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