Neuronal Dynamics：Two dimensions model 实验结果展示

一、演示效果和代码

本次实验以Morris-Lecar model 和 FitzHugh-Nagumo model两种模型为例研究了模型w,u随t变化的图像。
输出结果如下（蓝色线为$\frac{du}{dt}=0$,绿色线为$\frac{dw}{dt}=0$,黑色的线为(u,w)随时间t的变化轨迹曲线）：

代码如下：

import numpy as np
import matplotlib.pyplot as plt
class two_dimensions_model():
    #type=0 is Morris-Lecar model
    #type=1 is FitzHugh-Nagumo model
    def __init__(self):
        self.C=20
        self.Vl=-50
        self.V1=100
        self.V2=-70
        self.gl=2
        self.g1=4
        self.g2=8
        self.u1=0
        self.u2=15
        self.u3=10
        self.u4=10
        self.tw=0.1
        self.type=0
        self.b0=0
        self.b1=1
        self.I=0
    def m0u(self,u):
        return (1+np.tanh((u-self.u1)/self.u2))/2
    def w0u(self,u):
        return (1+np.tanh((u-self.u3)/self.u4))/2
    def tu(self,u):
        return self.tw/np.cosh((u-self.u3)/2/self.u4)
    def dudt(self,u,w):
        if self.type==0:
            return 1/self.C*(-self.g1*self.m0u(u)*(u-self.V1)-self.g2*w*(u-self.V2)-self.gl*(u-self.Vl)+self.I)
        elif self.type==1:
            return  u-u*u*u/3-w+self.I
    def dwdt(self,u,w):
        if self.type==0:
            return -(w-self.w0u(u))*self.tu(u)
        else:
            return self.b0+self.b1*u-w
    def plot_u_w_0_line(self,a,b,max_dif=0.1):
        x, y = np.meshgrid(a, b)
        x = x.T
        y = y.T
        imax = len(x)
        jmax = len(x[0])
        u = [[0 for j in range(jmax)] for i in range(imax)]
        w = [[0 for j in range(jmax)] for i in range(imax)]
        for i in range(imax):
            for j in range(jmax):
                i0 = x[i][j]
                j0 = y[i][j]
                u[i][j] = self.dudt(i0, j0)
                w[i][j] = self.dwdt(i0, j0)
        u1 = []
        w1 = []
        u2 = []
        w2 = []
        for i in range(imax):
            minu = np.min(np.abs(u[i]))
            minw = np.min(np.abs(w[i]))
            if minu < max_dif:
                j = np.where(minu == np.abs(u[i]))
                u1.append(x[i][j])
                w1.append(y[i][j])
            if minw < max_dif:
                j = np.where(minw == np.abs(w[i]))
                u2.append(x[i][j])
                w2.append(y[i][j])
        plt.plot(u1, w1, color="b")
        plt.plot(u2, w2, color="g")
    def plot_vector(self, a, b):
        x, y = np.meshgrid(a, b)
        x = x.T
        y = y.T
        imax = len(x)
        jmax = len(x[0])
        u = [[0 for j in range(jmax)] for i in range(imax)]
        w = [[0 for j in range(jmax)] for i in range(imax)]
        for i in range(imax):
            for j in range(jmax)