Use each file as a jupyter notebook cell. First copy and run the contents of auxiliar_functions.py.

auxiliar_functions.py

%matplotlib inline

from scipy.integrate import odeint
import matplotlib.pyplot as plt
import numpy as np

# Print function
def print_results(soln, time):
    show = 5
    def get_head_and_tail(vector):
        return np.concatenate([vector[:show], vector[-show:]])
    print_count = 1
    print("Values: ")
    for t, val in zip(get_head_and_tail(time), get_head_and_tail(soln)):
        print("[ x1({t:0.2f}), x2({t:0.2f})] = [{x1:0.2f}, {x2:0.2f}]".format(t=t, x1=val[0], x2=val[-1]))
        if print_count == show:
            print("...")
        print_count += 1
        
# Plot function
def plot_results(soln, time):
    # TODO: aesthetcics and formatting.
    plt.figure(figsize=(15,6))
    plt.plot(time,soln[:,0])
    plt.plot(time,soln[:,-1])
    plt.show()

first_ex.py

print("Ex 1) [add description] \n")


# Update function
def step(prev_xs, t, a, b):
    x1, x2 = prev_xs[0], prev_xs[-1]
    return [a * x2, -b * x1]

# Initial conditions
initial_values = [5, 5]
time = np.linspace(0,50, 500)

# Solution
soln = odeint(step, initial_values, time, args=(1, 1))

# Print results
print_results(soln, time)
    
# Plot results
plot_results(soln, time)

second_ex.py

print("Ex 2) [add description] \n")


# Update function
def step(prev_xs, t, a, b):
    x1, x2 = prev_xs[0], prev_xs[-1]
    return [-a * x1 + b * x2, b * x1 - a * x2]

# ----------------------------------------------
# a) 
print("A) initial values = (2, 1) and (a,b) = (2, 1)\n")

# Initial conditions
initial_values = [2, 1]
time = np.linspace(0,50, 500)

# Solution
soln = odeint(step, initial_values, time, args=(2,1))

# Print results
print_results(soln, time)
    
# Plot results
plot_results(soln, time)

# ----------------------------------------------
# b) 
print("B) initial values = (-2, 1) and (a,b) = (2, 1)\n")

# Initial conditions
initial_values = [-2, 1]
time = np.linspace(0,50, 500)

# Solution
soln = odeint(step, initial_values, time, args=(2,1))

# Print results
print_results(soln, time)
    
# Plot results
plot_results(soln, time)