Python Lotka–Volterra Equations

Python implementation of Lotka–Volterra Equations.

# © 2019 TheFlyingKeyboard and released under MIT License 
# theflyingkeyboard.net

from matplotlib import pyplot as plt
from matplotlib.ticker import FuncFormatter
from pylab import rcParams

x = 10
y = 5

a = 0.9
b = 0.1
c = 0.1
d = 0.4

step = 0.00001  # the smaller the more precise plots are
epochs = 100

xOverTime = []
yOverTime = []

for i in range(int(1 / step) * epochs):
    xOverTime.append(x)
    yOverTime.append(y)

    deltaX = a * x - b * x * y
    deltaY = c * x * y - d * y

    x += step * deltaX
    y += step * deltaY

rcParams['figure.figsize'] = 16, 9

plt.gca().xaxis.grid(True)
plt.gca().yaxis.grid(True)

plt.gca().get_xaxis().set_major_formatter(FuncFormatter(lambda x, p: format(int(x * step), ',')))

plt.xlabel("Epoch")
plt.ylabel("Population")

plt.plot(xOverTime, label="Prey")
plt.plot(yOverTime, label="Predator")

plt.legend(loc='upper right')
plt.show()

plt.gca().xaxis.grid(True)
plt.gca().yaxis.grid(True)

plt.plot(xOverTime, yOverTime)

plt.xlabel("Prey")
plt.ylabel("Predator")

plt.show()