In dynamics, the Van der Pol oscillator (named for Dutch physicist Balthasar van der Pol) is a type of nonconservative oscillator with nonlinear damping. It evolves in time according to the differential equation:

$\{d^2x\; \backslash over\; dt^2\}-\backslash mu(1-x^2)\{dx\; \backslash over\; dt\}+x=\; 0$

where x is the position coordinate — which is a function of the time t, and μ is a scalar parameter indicating the strength of the nonlinear damping. It can be proven via Liénard's Theorem that there exists a limit cycle for the undriven Van der Pol oscillator, thus making it an example of a Liénard system.

References

• Van Der Pol Oscillator Interactive Demonstrations

Chaotic maps

ファン・デル・ポール振動子