【SNN脉冲神经网络2】AdEx神经网络软件仿真-拓冰建站

本文使用AdEx神经元搭建一个完整的神经网络来进行生物神经脉冲现象的仿真。主要的目的是为了验证数学原理，因此只调用的numpy函数包。对应的代码例程如下：

1.导入所需的Python函数库

import numpy as np
import matplotlib.pyplot as plt
import re
import os

2.定义均值函数以及一些常用函数

def bin_data(data):try:    return np.mean(data[len(data)-bin_num:len(data)])except:return data[len(data)-1]def extract_number_from_string(s):match = re.search(r'_(\d+)$', s)if match:return int(match.group(1))else:return None

3.AdEx神经元定义

class AdExNeuron:def __init__(self, name, V_Neuron, w_adaptive, G_Synapsis_Excitatory, G_Synapsis_Inhibitory, E_Excitatory, E_Inhibitory, E_local, G_local, V_disturb, V_Excitatory_Threshold,C_Membrane, a_w_adaptive, tau_w_adaptive,tau_Synapsis,V_Reset_Threshold, V_Reset, b_w_adaptive,I_Synapsis, T_refractory, T_rest,Connecting_Neuron, Q_Synapsis, Probability_Connecting):# variable parametersself.name = nameself.V_Neuron = V_Neuronself.w_adaptive = w_adaptiveself.G_Synapsis_Excitatory = G_Synapsis_Excitatoryself.G_Synapsis_Inhibitory = G_Synapsis_Inhibitory# fixed parametersself.E_Excitatory = E_Excitatoryself.E_Inhibitory = E_Inhibitoryself.E_local = E_localself.G_local = G_localself.V_disturb = V_disturbself.V_Excitatory_Threshold = V_Excitatory_Thresholdself.C_Membrane = C_Membraneself.T_refractory = T_refractory# adaptive parametersself.a_w_adaptive = a_w_adaptiveself.tau_w_adaptive = tau_w_adaptiveself.tau_Synapsis = tau_Synapsis# reset parametersself.V_Reset_Threshold = V_Reset_Thresholdself.V_Reset = V_Resetself.b_w_adaptive = b_w_adaptiveself.I_Synapsis = I_Synapsisself.T_rest = T_rest# connecting neuronsself.Connecting_Neuron = Connecting_Neuronself.Q_Synapsis = Q_Synapsisself.Probability_Connecting = Probability_Connectingdef refresh_w_adaptive(self):# if self.T_rest<=0:self.w_adaptive = self.w_adaptive+dt*(self.a_w_adaptive*(self.V_Neuron-self.E_local)-self.w_adaptive)/self.tau_w_adaptivedef refresh_G_Synapsis_Excitatory(self):# if self.T_rest<=0:self.G_Synapsis_Excitatory = self.G_Synapsis_Excitatory-dt*self.G_Synapsis_Excitatory/self.tau_Synapsisdef refresh_G_Synapsis_Inhibitory(self):# if self.T_rest<=0:self.G_Synapsis_Inhibitory = self.G_Synapsis_Inhibitory-dt*self.G_Synapsis_Inhibitory/self.tau_Synapsisdef refresh_membrane_potential(self):if self.T_rest<=0:self.V_Neuron =self.V_Neuron+dt*(self.G_Synapsis_Excitatory*(self.E_Excitatory-self.V_Neuron)+self.G_Synapsis_Inhibitory*(self.E_Inhibitory-self.V_Neuron)+self.G_local*(self.E_local-self.V_Neuron)+self.G_local*self.V_disturb*np.exp((self.V_Neuron-self.V_Excitatory_Threshold)/self.V_disturb)-self.w_adaptive+self.I_Synapsis)/self.C_Membraneelse:self.T_rest=self.T_rest-dtself.refresh_w_adaptive()self.refresh_G_Synapsis_Excitatory()self.refresh_G_Synapsis_Inhibitory()def fire(self, num1, num2):global fire_matrix# refresh self parameterself.V_Neuron = self.V_Resetself.w_adaptive = self.w_adaptive+self.b_w_adaptiveself.T_rest=self.T_refractory# refresh the G_Synapsis# print(self.name)if self.name[1]=='1':num1=num1+1fire_matrix1[extract_number_from_string(self.name)-1,test_input_index]=2for neuron1 in self.Connecting_Neuron:neuron1.G_Synapsis_Inhibitory=neuron1.G_Synapsis_Inhibitory+self.Q_Synapsisif self.name[1]=='2':num2=num2+1fire_matrix2[extract_number_from_string(self.name)-1,test_input_index]=2for neuron2 in self.Connecting_Neuron:neuron2.G_Synapsis_Excitatory=neuron2.G_Synapsis_Excitatory+self.Q_Synapsisreturn num1, num2def judge_fire(self, num1, num2):if self.V_Neuron>self.V_Reset_Threshold:num1, num2=self.fire(num1, num2)else:passreturn num1, num2def Add_Synapsis(self, Synapsis):self.Connecting_Neuron.append(Synapsis)

4.连接神经元

for neuron_front in G_Group:for neuron_back in G_Group:if neuron_front !=neuron_back:if np.random.rand()<neuron_front.Probability_Connecting:neuron_front.Connecting_Neuron.append(neuron_back)

5.将神经元接入输入

for neuron_front in P2_Group:for neuron_back in G_Group:if neuron_front !=neuron_back:if np.random.rand()<neuron_front.Probability_Connecting:neuron_front.Connecting_Neuron.append(neuron_back)

6.定义输入函数脉冲

def heaviside(x):return 0.5 * (1 + np.sign(x))
def input_rate(t, t1_exc, tau1_exc, tau2_exc, ampl_exc, plateau):# t1_exc=10. # time of the maximum of external stimulation# tau1_exc=20. # first time constant of perturbation = rising time# tau2_exc=50. # decaying time# ampl_exc=20. # amplitude of excitationinp = ampl_exc * (np.exp(-(t - t1_exc) ** 2 / (2. * tau1_exc ** 2)) * heaviside(-(t - t1_exc)) +heaviside(-(t - (t1_exc+plateau))) * heaviside(t - t1_exc) +np.exp(-(t - (t1_exc+plateau)) ** 2 / (2. * tau2_exc ** 2)) * heaviside(t - (t1_exc+plateau)))return inp

7.开始仿真

for tick_time in np.arange(0, TotTime, dt):fire_probability=dt*test_input[test_input_index]if test_input_index%5000==0:print(test_input_index)print("fire_probability:"+str(fire_probability))for neuron in P2_Group:if np.random.rand()<fire_probability:neuron.fire(0,0)fire1_num=0fire2_num=0fire1_frequent=0fire2_frequent=0for neuron in G_Group:neuron.refresh_membrane_potential()fire1_num, fire2_num=neuron.judge_fire(fire1_num, fire2_num)fire1_frequent=fire1_num/dt/N1fire2_frequent=fire2_num/dt/N2fire1_result.append(fire1_frequent)fire2_result.append(fire2_frequent)neuron1_potential_bin.append(G1_1.V_Neuron) # type: ignoreneuron2_potential_bin.append(G2_1.V_Neuron) # type: ignorefire1_result_bin.append(bin_data(fire1_result))fire2_result_bin.append(bin_data(fire2_result))test_input_index=test_input_index+1

8.仿真结果

下面顺序依次是：

兴奋性神经元与抑制性神经元的膜电位

输入点火频率与两类神经元的点火频率

总体点火频率与对应神经元点火节点