  Cilia and flagella are essential building blocks for biological fluid
transport and locomotion at the micron scale. They often beat in synchrony and
may transition between different synchronization modes in the same cell type.
Here, we investigate the behavior of elastic microfilaments, protruding from a
surface and driven at their base by a configuration-dependent torque. We
consider full hydrodynamic interactions among and within filaments and no slip
at the surface. Isolated filaments exhibit periodic deformations, with
increasing waviness and frequency as the magnitude of the driving torque
increases. Two nearby but independently-driven filaments synchronize their
beating in-phase or anti-phase. This synchrony arises autonomously via the
interplay between hydrodynamic coupling and filament elasticity. Importantly,
in-phase and anti-phase synchronization modes are bistable and co-exist for a
range of driving torques and separation distances. These findings are
consistent with experimental observations of in-phase and anti-phase
synchronization in the biflagellate \textit{Chlamydomonas reinhardtii} and
could have important implications on understanding the biophysical mechanisms
underlying transitions between multiple synchronization modes.
