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Concept# Van der Pol oscillator

Summary

In the study of dynamical systems, the van der Pol oscillator (named for Dutch physicist Balthasar van der Pol) is a non-conservative, oscillating system with non-linear damping. It evolves in time according to the second-order differential equation
{d^2x \over dt^2} - \mu(1-x^2){dx \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 nonlinearity and the strength of the damping.
History
The Van der Pol oscillator was originally proposed by the Dutch electrical engineer and physicist Balthasar van der Pol while he was working at Philips. Van der Pol found stable oscillations, which he subsequently called relaxation-oscillations and are now known as a type of limit cycle, in electrical circuits employing vacuum tubes. When these circuits are driven near the limit cycle, they become entrained, i.e. the driving signal pulls the c

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