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lotka_volterra.py
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lotka_volterra.py
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"""
Solution for the Lotka-Volterra equations (predator-prey model)
"""
import numpy as np
from scipy import integrate
import matplotlib.pyplot as plt
# declare initial values
preys = 4
predators = 2
X0 = [preys, predators]
t = np.arange(1, 20, .1)
a = 1
b = 1
c = 1
d = 1
def model(N, t):
"""Model for the Lotka-Volterra equations
parameters:
x: no. preys
y: no. predators
t: time (independent variable)
a, b, c, d: arbitary constants for the differential equations
"""
x, y = N
# equation for the no. preys over time
dxdt = (a - b*y) * x
# equation for the no. predators over time
dydt = (c*x - d) * y
# returns the set of differential equations
return [dxdt, dydt]
solution = integrate.odeint(model, X0, t)
x, y = solution.T
fig, ax = plt.subplots(1, 2)
ax[0].plot(t, x); ax[0].plot(t, y)
ax[0].set_title("Population size in time")
ax[0].set_ylabel("no. species")
ax[0].set_xlabel("time")
ax[1].plot(x, y)
ax[1].set_title("Population size in phase space")
ax[1].set_ylabel("no. preys")
ax[1].set_xlabel("no. predators")
ax[0].grid(); ax[1].grid()
plt.show()