Robust formation of metachronal waves in directional chains of phase oscillators

Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearestneighbor interactions, connected in a loop and with rotational symmetry, so each oscillator resembles every other oscillator in the chain. Numerical integrations of the discrete phase oscillator systems and a continuum approximation show that directional models (those that do not obey reversal symmetry), can exhibit instability to short wavelength perturbations but only in regions where the slope in phase has a particular sign. This causes short wavelength perturbations to develop that can vary the winding number that describes the sum of phase differences across the loop and the resulting metachronal wave speed. Numerical integrations of stochastic directional phase oscillator models show that even a weak level of noise can seed instabilities that resolve into metachronal wave states.

Automated summary

Biological systems can use the collective formation of a metachronal wave to achieve locomotion and fluid transport. One-dimensional chains of phase oscillators connected in a loop with rotational symmetry can exhibit instability to short wavelength perturbations, leading to changes in the metachronal wave speed. Stochastic phase oscillator models also show that even weak noise can induce instabilities that result in metachronal wave states.