  Biofilament-motor protein complexes are ubiquitous in biology and drive the
transport of cargo vital for many fundamental cellular processes. As they move,
motor proteins exert compressive forces on the filaments to which they are
attached, leading to buckling and a subsequent range of dynamics. The follower
force model, in which a single compressive force is imposed at the filament
tip, is the standard and most basic model for an elastic filament, such as a
microtubule, driven by a motor protein. Depending on the force value, one can
observe different states including whirling, beating and writhing, though the
bifurcations giving rise to these states are not completely understood. In this
paper, we utilise techniques from computational dynamical systems to determine
and characterise these bifurcations. We track emerging time-periodic branches
and identify new, quasiperiodic states. We investigate the effect of filament
slenderness on the bifurcations and, in doing so, present a comprehensive
overview of the dynamics which emerge in the follower force model.
