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The forced van der Pol equation. (English) Zbl 1297.97026

Summary: We report on a study of the forced van der Pol equation \[ \ddot x+\varepsilon(x^2-1)\dot x+x=F\cos\omega t \] by solving numerically the differential equation for a variety of values of the parameters \(\varepsilon,F\) and \(\omega\). In doing so, many striking and interesting trajectories can be discovered and phenomena such as frequency entrainment, almost periodic solutions, space filling trajectories and seemingly chaotic behaviour are explored. These examples naturally give rise to computer laboratory problems suitable for student research and small group projects.

MSC:

97I70 Functional equations (educational aspects)
97N40 Numerical analysis (educational aspects)
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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References:

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