Van der Pol oscillator, weakly nonlinear regime

Numerical solution to the Van der Pol equation, x''(t) - a [1 - x^2(t)] x'(t) + x(t) = 0, for a = 0.2 and initial conditions x(0) = 0.1; x'(0) = 0. Animation generated on Mathematica.
This is a good model of an approximately sinusoidal self-oscillator, like a pendulum clock. The first plot (top left) shows the solution x(t). The second (top right) shows the total mechanical energy in the oscillator (kinetic plus elastic potential). The last plot is the solution represented as a trajectory in Liénard phase space, with y(t) = x'(t) - a [x(t) - x^3(t)/3]. The dashed blue curve is the vertical isocline.