I have to draw the phase space of this modification of Duffing oscillator: \begin{align} \dot x &= y,\\ \dot y &= x - x^3 - ay - (x^2)y \quad \text{ when } \quad a=1 \; \text{ and } \;a=5. \end{align}
I know that critical points are $(0, 0)$, $(-1, 0)$, and $(1, 0),$ and I have demonstrated that when $a =1$ I have a spiral the form $(\pm1,0)$ and when $a = 5$ not.
Does someone know how to draw it?
Thank you.
$\endgroup$31 Answer
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generated with python:
import numpy as np import matplotlib.pyplot as plt xmin, xmax = -2.0, 2.0 ymin, ymax = -1.0, 1.0 x, y = np.meshgrid(np.linspace(xmin, xmax, 30, endpoint = True), np.linspace(ymin, ymax, 30, endpoint = True)) a = 1 u = y v = x - x**3 - a * y - x**2 * y plt.streamplot(x, y, u, v) plt.show() 
