Interactive continuous plotting of an ODE model in Python

Question

I would like to create a script that integrates an ode model, such that I can change one of the parameters and see the response of the systems to this change. If for, for example, I have a Lotka-Volterra model (as taken from this example):

import numpy as np
from scipy import integrate
a = 1.
b = 0.1
c = 1.5
d = 0.75

def dX_dt(X, t=0):
    """ Return the growth rate of fox and rabbit populations. """
    return array([ a*X[0] -   b*X[0]*X[1] ,  
                  -c*X[1] + d*b*X[0]*X[1] ])

t = np.linspace(0, 15,  1000)              # time
X0 = np.array([10, 5])    # initials conditions: 10 rabbits and 5 foxes  

X, infodict = integrate.odeint(dX_dt, X0, t, full_output=True)

I would like to create a slider for parameters a and c, as in the slider_demo of matplotlib, or any other tool. The plot should display a certain window of time that always spans [t_current - delta_t ,t_current]. And so I will be able to explore the parameters space continuously by changing the sliders of the parameters.

How to do it?

Ed Smith · Accepted Answer · 2016-04-21 09:54:50Z

You have all the pieces, basically just change the update method in the widget example to recalculate the integral of dX_dt using the new value based on the sliders and then use this to set the y line values. The code would look like:

import numpy as np
from scipy import integrate
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider, Button, RadioButtons

b = 0.1
d = 0.75
a=1
c=1.5
def dX_dt(X, t=0, a=1, c=1.5):
    """ Return the growth rate of fox and rabbit populations. """
    return np.array([ a*X[0] -   b*X[0]*X[1] ,  
                     -c*X[1] + d*b*X[0]*X[1] ])


t = np.linspace(0, 15,  1000)              # time
X0 = np.array([10, 5])          # initials conditions: 10 rabbits and 5 foxes  

fig, ax = plt.subplots()
plt.subplots_adjust(left=0.25, bottom=0.25)

l1, l2 = plt.plot(t, integrate.odeint(dX_dt, X0, t, (a, c)))

axcolor = 'black'
ax_a = plt.axes([0.25, 0.1, 0.65, 0.03], axisbg=axcolor)
ax_c = plt.axes([0.25, 0.15, 0.65, 0.03], axisbg=axcolor)

sa = Slider(ax_a, 'a', 0.1, 10.0, valinit=1)
sc = Slider(ax_c, 'c', 0.1, 10.0, valinit=1.5)


def update(val):
    a = sa.val
    c = sc.val
    x = integrate.odeint(dX_dt, X0, t, (a, c))
    l1.set_ydata(x[:,0])
    l2.set_ydata(x[:,1])
    fig.canvas.draw_idle()

sa.on_changed(update)
sc.on_changed(update)

plt.show()

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