In [1]:

    

import numpy as np
from scipy import integrate
import matplotlib.pyplot as plt
%matplotlib inline

def dX_dt(X, t=0):
    R = X[0]
    F = X[1]
    alpha, beta, gamma, delta = parameters
    dRdt = alpha * R - beta * F * R
    dFdt = gamma * R * F - delta * F
    res = [dRdt,dFdt]
    return np.array(res)

# initial condition
X0 = [20.,10.]
parameters = (.2, .01, .001, .1)
t = np.linspace(0,100,1000)
X, infodict = integrate.odeint(dX_dt, X0, t, full_output=True)
infodict['message']


    

    
Out[1]:





'Integration successful.'

In [2]:

    

rabbits, foxes = X.T


    

In [3]:

    

plt.plot(t, rabbits, label='Rabbits')
plt.plot(t, foxes, label='Foxes')
plt.xlabel('Time')
plt.ylabel('Population')
plt.legend()
plt.grid(linestyle='dotted')


    

In [4]:

    

plt.plot(rabbits, foxes)
plt.xlabel('Rabbits')
plt.ylabel('Foxes')
plt.grid(linestyle='dotted')


    

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In [6]:

    

X.T[:, -1]


    

    
Out[6]:





array([ 12.64881348,  19.20161261])

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