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Biofilament-motor protein complexes are ubiquitous in biology and drive thetransport of cargo vital for many fundamental cellular processes. As they move,motor proteins exert compressive forces on the filaments to which they areattached, leading to buckling and a subsequent range of dynamics. The followerforce model, in which a single compressive force is imposed at the filamenttip, is the standard and most basic model for an elastic filament, such as amicrotubule, driven by a motor protein. Depending on the force value, one canobserve different states including whirling, beating and writhing, though thebifurcations giving rise to these states are not completely understood. In thispaper, we utilise techniques from computational dynamical systems to determineand characterise these bifurcations. We track emerging time-periodic branchesand identify new, quasiperiodic states. We investigate the effect of filamentslenderness on the bifurcations and, in doing so, present a comprehensiveoverview of the dynamics which emerge in the follower force model.

Bifurcations and nonlinear dynamics of the follower force model for active filaments