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Carpets of actively bending cilia represent arrays of biological oscillatorsthat can exhibit self-organized metachronal synchronization in the form oftraveling waves of cilia phase. This metachronal coordination supposedlyenhances fluid transport by cilia carpets. Using a multi-scale model calibratedby an experimental cilia beat pattern, we predict multi-stability of wavemodes. Yet, a single mode, corresponding to a dexioplectic wave, haspredominant basin-of-attraction. Similar to a "dynamic" Mermin-Wagner theorem,relaxation times diverge with system size, which rules out global order ininfinite systems. In finite systems, we characterize the synchronizationtransition as function of quenched frequency disorder, using generalizedKuramoto order parameters. Our framework termed Lagrangian Mechanics of ActiveSystems allows to predict the direction and stability of metachronalsynchronization for given beat patterns.

Synchronization in cilia carpets: multiple metachronal waves are stable, but one wave dominates