Dynamics of a deformable self-propelled particle in three dimensions

We investigate the dynamics of a self-propelled particle in three dimensions by solving numerically the time-evolution equations for the center of mass and a tensor variable characterizing the deformations around the spherical shape. There are successive bifurcations in the dynamics caused by changing the parameters. A straight motion becomes unstable and a rotating motion on a plane appears. After this rotating motion becomes unstable, a helical motion occurs. A linear stability analysis of these solutions is carried out to determine the bifurcation thresholds, which is in a good agreement with the numerical results.