Dynamics of a System of Two Coupled Oscillators Driven by a Third Oscillator - Lazarus, Lauren; Rand, Richard H. (Journal of Applied Nonlinear Dynamics, 2026)
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 presence of numerous bifurcation curves defines parameter regions with 2, 4, or 6 solutions corresponding to phase locking. 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.