Collective dynamics and synchronization of coupled hair-bundle models with elastic and viscous interactions.

Despite extensive studies of single hair-bundle dynamics, comparatively little attention has been paid to the collective dynamics arising in coupled hair-bundle systems. In this work, we investigate the collective dynamics of coupled hair bundles using a simplified dimensionless mechanical model that captures the essential nonlinear features of hair-bundle activity. We focus on two physically motivated interaction mechanisms: elastic and viscous coupling between neighboring bundles. The stability of synchronized motion is first analyzed using the master stability function framework and complemented by extensive numerical simulations. Our results demonstrate that within the present model, viscous coupling is significantly more effective than elastic coupling in promoting stable synchronization across a wide range of system parameters. Beyond complete synchronization, the network exhibits a variety of complex collective states, including non-stationary chimera patterns and clustered dynamics with distinct dynamical behaviors. Finally, we establish the occurrence of coherence resonance in the network, showing that an intermediate level of noise can enhance temporal regularity in the absence of external periodic forcing. These findings provide new insights into the mechanisms governing collective phenomena in interacting hair-bundle systems.