Solving and plotting ODE with dependent parameters

Question

I'm working on a bit of code where I have the following system of equations here. The issue being that I'd very much like to solve for multiple values of k as well as have a phase plane/quiver plot for each value of k. Can someone please help me? This is what I have so far for the solver:

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

def model(X, t):
    x = X[0]
    y = X[1]
    dxdt = k*x - y
    dydt = x + y
    return [dxdt, dydt]
#Initial state 
X0 = [1,1]

#Time
t = np.linspace(0,10)

X = odeint(model, X0, t)

And this is what I have so far for plotting:

x = X[:,0]
y = X[:,1]

plt.plot(x,y)

Please note, I'm not trying to simply solve the system! I'm trying to solve it with multiple values changing (k) and plotting the resulting equations.

Answer 1

You have to iterate over k, and pass the value as an additional parameter:

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

def model(X, t, k):
    x = X[0]
    y = X[1]
    dxdt = k*x - y
    dydt = x + y
    return [dxdt, dydt]
#Initial state 
X0 = [1,1]

#Time
t = np.linspace(0,10)
Ks = np.linspace(-1, 1, 10)

for kix in Ks:
    X = odeint(model, X0, t, args=(kix,))
    x = X[:,0]
    y = X[:,1]
    plt.plot(x,y)
plt.show()