phaseplanep&a.py

import numpy as np
import matplotlib.pyplot as plt


# Function to calculate the population of pythons and alligators at each time step
def calculate_population_dynamics(r1, r2, ϱ1, ϱ2, P0, A0, m, t):
    popP = [P0]  # List to store python population sizes
    popA = [A0]  # List to store alligator population sizes

    for i in range(1, t + 1):
        tempP = (1 + r1) * popP[i - 1] - ϱ1 * popP[i - 1] * popA[i - 1] + m
        popP.append(tempP)

        tempA = (1 + r2) * popA[i - 1] - ϱ2 * popP[i - 1] * popA[i - 1]
        popA.append(tempA)

    return popP, popA


# Parameter values
r1 = 0.005
r2 = 0.005
ϱ1 = 0.0005
ϱ2 = 0.0005
P0 = 100
A0 = 100
m = 5
t = 100

# Calculate population dynamics
python_pop, alligator_pop = calculate_population_dynamics(r1, r2, ϱ1, ϱ2, P0, A0, m, t)

# Create phase plane plot
plt.plot(python_pop, alligator_pop)
plt.xlabel("Number of Pythons")
plt.ylabel("Number of Alligators")
plt.title("Phase Plane: Pythons vs Alligators")
plt.grid(True)
plt.show()