Coupled Oscillators: Kuramoto Synchronization + Chimera States

When do coupled phase oscillators fall into step, and when do they fracture? The Kuramoto model gives the classic synchronization transition — followed here across all-to-all, Erdős–Rényi, and scale-free topologies, with onset matched to the analytic critical coupling K_c = 2σ√(2/π). Introducing a phase lag and finite interaction range (Kuramoto–Sakaguchi on a ring) opens a stranger possibility: chimera states, where synchronized and incoherent populations coexist on an identical ring. A sweep of the (K, R) plane then maps the full landscape from global synchrony through chimera to incoherence. Built in Julia as an interactive Pluto notebook.