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van der Pol Equation

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vanderPolEquation

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an equation describing self-sustaining oscillations in which energy is fed into small oscillations and removed from large oscillations. This equation arises in the study of circuits containing vacuum tubes and is given by

y^('')-mu(1-y^2)y^'+y=0.

If mu=0, the equation reduces to the equation of simple harmonic motion

y^('')+y=0.

See also

Rayleigh Differential Equation, Simple Harmonic Motion

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References

Birkhoff, G. and Rota, G.-C. Ordinary Differential Equations, 3rd ed. New York: Wiley, p. 134, 1978.Boyce, W. E. and DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems, 4th ed. New York: Wiley, 1986.Kreyszig, E. Advanced Engineering Mathematics, 6th ed. New York: Wiley, pp. 496-500, 1988.Wiggins, S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. New York: Springer-Verlag, p. 179, 1990.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 127, 1997.

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van der Pol Equation

Cite this as:

Weisstein, Eric W. "van der Pol Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/vanderPolEquation.html

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