= Synchronization of oscillators
<Synchronization of oscillators> occurs when interacting or driven <oscillators> acquire a sustained relation between their <phases> or frequencies. Equal amplitudes are not required. In one simple phase model, a relative phase $\psi$ obeys $\dot\psi=\Delta\omega-K\sin\psi$, where $\Delta\omega$ is the uncoupled frequency mismatch and $K>0$ the coupling strength.
When $|\Delta\omega|<K$, a fixed relative phase exists; the branch with $\cos\psi>0$ is stable because the linearized restoring coefficient is $-K\cos\psi$. The <Kuramoto model> extends this competition between mismatch and coupling to a population of <phase oscillators>.<From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators by Steven H. Strogatz>[Sections 2–3, phase reduction and collective synchronization]{ref}
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