Citation
Chemical Oscillations, Waves, and Turbulence
TL;DR
Synchronization emerges as a phase transition when coupling strength exceeds a critical threshold
Kuramoto's mathematical model of coupled oscillators provides rigorous foundations for understanding synchronization as an emergent phenomenon. The model shows how synchronization emerges suddenly (through phase transition) rather than gradually, and predicts the critical threshold of coupling strength required for synchronization to occur.
This work explains phenomena ranging from firefly synchronization to neural oscillations to circadian rhythms. For organizations, it offers insight into how coordination emerges in distributed systems and why some threshold level of interaction or coupling may be required before coordinated behavior appears.
Key Findings from Kuramoto (1984)
- Synchronization emerges as a phase transition when coupling strength exceeds a critical threshold
- Below threshold, systems remain desynchronized indefinitely; above threshold, synchronization emerges rapidly
- The model applies across biological, chemical, and physical systems
- Weak coupling, repeated over many individuals, can produce strong collective synchronization