Cilia and flagella are organelles that play central roles in unicellular locomotion, embryonic
development, and fluid transport around tissues. In these examples, multiple cilia are often found
in close proximity and exhibit coordinated motion. Inspired by the flagellar motion of biflagellate
cells, we examine the synchrony exhibited by a filament pair surrounded by a viscous fluid and
tethered to a rigid planar surface. A geometrically-switching base moment drives filament motion,
and we characterize how the stability of synchonized states depends of the base torque magnitude.
In particular, we study the emergence of bistability that occurs when the anti-phase, breast-stroke
branch becomes unstable. Using a bisection algorithm, we find the unstable edge-state that exists
between the two basins of attraction when the system exhibits bistability. We establish a bifurcation
diagram, study the nature of the bifurcation points, and find that the observed dynamical system
can be captured by a modified version of Adler’s equation. The bifurcation diagram and presence
of bistability reveal a simple mechanism by which the anti-phase breast stroke can be modulated, or
switched entirely to in-phase undulations through the variation of a single bifurcation parameter.