Arnold tongue

Summary

An Arnold tongue is a region in the parameter plane of the circle map where the rotation number takes one fixed rational value $p/q$. Each tongue starts at the single point $\Omega = p/q$ when there is no nonlinearity, and widens as the nonlinearity $K$ grows. Inside a tongue the system is mode locked: it has periodic orbits of period $q$. Arnold tongues describe synchronization of oscillators with a periodic forcing.