izhikevich_model.py

# -*- coding: utf-8 -*-
"""
Simulate Izhikevich model and draw graph
Created on Tue Mar 01 04:21:25 2016

@author: nebula
"""

import numpy as np
import matplotlib.pyplot as plt


class Iz():
    def __init__(self, tmax=200, dt=0.1, stimarray=None,
                 a = 0.02, b = 0.2, c=-50.0, d= 2.0, title='Izhikevich Model'):
        self.maxstep = int(tmax/dt)
        self.record = {}
        self.record['t'] = np.linspace(0, tmax, self.maxstep)
        self.record['v'] = -65.0 * np.ones(self.maxstep)

        self.dt = dt
        self.t = 0.0
        self.v = -65.0
        self.a = a
        self.b = b
        self.c = c
        self.d = d
        self.i = 10.0
        self.u = self.v * self.b
        self.finish_init = 20
        
        self.title = title
        
    
    def _delta_v(self, i=0.0):
        return 0.04 * self.v * self.v + 5 * self.v + 140 - self.u + i
    
    def _delta_u(self):
        return self.a * (self.b * self.v - self.u)

    def run(self):
        for i in range(self.maxstep):
            self.t = self.dt * i
            if self.t < self.finish_init:
                delta_v = self._delta_v(i=0)
            else:
                delta_v = self._delta_v(i=self.i)                
            
            delta_u = self._delta_u()
            
            self.v += delta_v * self.dt
            self.u += delta_u * self.dt

            if self.v > 30:
                self.v = self.c
                self.u = self.u + self.d
                
            
            self.record['t'][i] = i*self.dt
            self.record['v'][i] = self.v

        self.plot()

    def show(self):
        print(self.record['t'])
        print(self.record['v'])


    def plot(self):
        plt.figure(figsize=(20, 10))

        plt.plot(self.record['t'], self.record['v'], color='black')
        if self.title is not None:
            plt.title(self.title)
        plt.ylim(-80, 40)
        plt.xlabel('$t$ [msec]')
        plt.ylabel('$V$ [mV]')
        plt.rcParams['font.size'] = 28
        plt.grid(True)
        plt.show()
    

if __name__ == '__main__':
    # regular spiking (RS)
    iz = Iz(a= 0.02, b=0.2, c=-65, d=8, title='Regular Spiking (RS)\n$a=0.02,\, b=0.2,\, c=-65.0,\, d=8$')
    iz.run()

    # Intrinsically bursting (IB)    
    iz = Iz(a= 0.02, b=0.2, c=-55, d=4.0, title='Intrinsically Bursting (IB)\n$a=0.02,\, b=0.2,\, c=-55,\, d=4.0$')
    iz.run()

    # Chattering (CH)
    iz = Iz(a= 0.02, b=0.2, c=-50, d=2.0, title='Chattering (CH)\n$a=0.02,\, b=0.2,\, c=-50.0,\, d=2.0$')
    iz.run()

    # fast spiking (FS)    
    iz = Iz(a= 0.1, b=0.2, c=-65, d=2.0, title='Fast Spiking (FS)\n$ a=0.1,\, b=0.2,\, c=-65.0,\, d=2.0$')
    iz.run()