Individual and collective dynamics of self-propelled soft particles

Deformable self-propelled particles provide us with one of the most important nonlinear dissipative systems, which are related, for example, to the motion of microorganisms. It is emphasized that this is a subject of localized objects in non-equilibrium open systems. We introduce a coupled set of ordinary differential equations to study various dynamics of individual soft particles due to the nonlinear couplings between migration, spinning and deformation. By introducing interactions among the particles, the collective dynamics and its collapse are also investigated by changing the particle density and the interaction strength. We stress that assemblies of self-propelled particles also exhibit a variety of non-equilibrium localized patterns. It is our great pleasure to dedicate the present article to Professor Helmut R. Brand on the occasion of his sixtieth birthday. Professor Brand has made outstanding efforts for the scientific interaction in the field of non-linear and non-equilibrium physics between Japan and Germany for the past thirty years.