Van der Pol equation

Let us consider the van der Pol equation [Verhulst (1996)]:

\begin{equation*} \ddot{x} + x = \mu (1 - x^2) \dot{x} , \end{equation*}
formulated around 1920 by Balthasar van der Pol to describe oscillations in a triode-circuit. With $x_1 = x$ and $x_2 = \dot{x}$, we obtain the following dynamical system, with parameter $\mu$:
\begin{equation*} \begin{cases} \dot{x}_1 = x_2 \\ \dot{x}_2 = -x_1 + \mu (1-x_1 ^2)x_2 \end{cases}. \end{equation*}
You can visualize the solution passing through $(1,~0)$ at $t = 0$: choose a value of $\mu$ (decimal number between $-1$ and $2$). For $\mu > 0$, the system has a stable limit cycle.

Simulation

$\mu =$ You must enter a decimal number between $-1$ and $2$.

Orbit of the van der Pol equation

Bibliography

F. Verhulst. Nonlinear differential equations and dynamical systems. Springer Science & Business Media, 1996.