Frequency Entrainment of a Forced van der Pol Oscillator

A van der Pol relaxation oscillator that is subjected to external sinusoidal forcing can exhibit stable and unstable periodic and almost periodic responses. For some forcing amplitudes it even happens that two stable subharmonics having different periods may coexist. We investigate here the stable responses of such forced oscillators. By numerically computing the rotation number of stable oscillations for various values of the forcing amplitude and oscillator tuning, we obtain descriptions of regions of phase locking, successive bifurcation of stable subharmonic and almost periodic oscillations, and overlap regions where two distinct stable oscillations can coexist.