
05609032
j
2009e.00520
Fay, Temple H.
The forced van der Pol equation.
Int. J. Math. Educ. Sci. Technol. 40, No. 5, 669677 (2009).
2009
Taylor \& Francis, Abingdon, Oxfordshire
EN
I75
N45
R25
forced van der Pol equation
harmonic and subharmonic solutions
limit cycles
numerical solutions
doi:10.1080/00207390902759568
Summary: We report on a study of the forced van der Pol equation $$\ddot x+\varepsilon(x^21)\dot x+x=F\cos\omega t$$ 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.