"""
A classical system of difference equations;
the Lotka-Volterra model. The model describes 
the dynamics of two interacting species;
one predator and one prey.
"""

import numpy as np
import matplotlib.pyplot as plt

x0 = 100              # startpopulasjon byttedyr
y0 = 8                # startpopulasjon rovdyr
a = 0.0015
b = 0.0003
c = 0.006
d = 0.5
N = 10000             # antall tidsenheter (dager)
time = range(N+1)
x = np.zeros(len(time))
y = np.zeros_like(x)

x[0] = x0
y[0] = y0

for n in time[1:]:
    x[n] = x[n-1] + a * x[n-1] - b * x[n-1] * y[n-1]
    y[n] = y[n-1] + d * b * x[n-1] * y[n-1] - c * y[n-1]

plt.plot(time, x,label = 'Byttedyr')
plt.plot(time, y, label = 'Rovdyr')
plt.xlabel('Tid')
plt.ylabel('Populasjon')
plt.legend()
plt.show()