DYNAMICS OF A SYSTEM OF TWO COUPLED OSCILLATORS WHICH ARE DRIVEN BY A THIRD OSCILLATOR

Analytical and numerical methods are applied to a pair of coupled nonidentical phase-only oscillators, where each is driven by the same independent third oscillator. The pres-ence of numerous bifurcation curves defines parameter re-gions with 2, 4, or 6 solutions corresponding to phase lock-ing. In all cases, only one solution is stable. Elsewhere, phase locking to the driver does not occur, but the average frequencies of the drifting oscillators are in the ratio of m:n. These behaviors are shown analytically to exist in the case of no coupling, and are identified using numerical integration when coupling is included