Simple Lotka-Volterra implementation

lotka-volterra.py

import numpy as np
import matplotlib.pyplot as plt

def xdot(x, y, alpha, beta, gamma, delta):
    """
    this function represents the rate of change of the prey population
    """
    return alpha * x  - beta * x * y

def ydot(x, y, alpha, beta, gamma, delta):
    """
    this function represents the rate of change of the predator population
    """
    return delta * x * y - gamma * y

T = 1000 # number of iterations
x = np.zeros(T) # allocating memory to save the system history
y = np.zeros(T)

x[0] = 10. # prey initial population
y[0] = 10. # predator initial population
dt = 0.01

# defining the parameters
params = {'alpha': 0.5, 
          'beta': 0.5,
          'delta': 0.5,
          'gamma': 0.5}

# time integration loop
for t in range(0,T-1):
    x[t+1] = x[t] + dt * xdot(x[t], y[t], **params)
    y[t+1] = y[t] + dt * ydot(x[t], y[t], **params)
    

# output and plots 
plt.plot(x, label='Presa', color='black', ls=':')
plt.plot(y, label='Predador', color='blue', ls='--')
plt.legend()
plt.xlabel('Time (a.u)')
plt.ylabel('Population')
#plt.savefig('result_lotka-volterra.png', dpi=300) # uncomment for saving to a png file
plt.show()
plt.plot(x, y)
plt.xlabel('presa')
plt.ylabel('predador')