Phase reduction of oscillators — PRC, entrainment, and Arnold tongues
Any limit cycle can be reduced to a phase equation: dφ/dt = ω₀ + ε·Z(φ)·I(t), where Z(φ) is the infinitesimal PRC and I(t) is the forcing. Synchronization occurs when the phase slip is zero. The Arnold tongue shows entrainment regions in (ε, ω) space.