van_der_pol

diffeqzoo.ivps.van_der_pol(*, stiffness_constant=1.0, initial_values=(2.0, 0.0), time_span=(0.0, 6.3))

Construct the Van-der-Pol system as a second-order differential equation.

The Van-der-Pol system is a non-conservative oscillator subject to non-linear damping. It is a popular benchmark problem, because it involves a parameter \(\mu\) (the “stiffness constant”) which governs the stiffness of the problem. For \(\mu ~ 1\), the problen is not stiff. For large values (e.g. \(\mu ~ 10^6\)) the problem is stiff. It was first published by Van der Pol (1920).

BibTex for Van der Pol (1920).

@article{van1920theory,
    title={Theory of the amplitude of free and forced triode vibrations},
    author={Van der Pol, Balthasar},
    journal={Radio Review},
    volume={1},
    pages={701--710},
    year={1920}
}