  We investigate the dynamical coupling between the motion and the deformation
of a single self-propelled domain based on two different model systems in two
dimensions. One is represented by the set of ordinary differential equations
for the center of gravity and two tensor variables characterizing deformations.
The other is an active cell model which has an internal mechanism of motility
and is represented by the partial differential equation for deformations.
Numerical simulations show a rich variety of dynamics, some of which are common
to the two model systems. The origin of the similarity and the difference is
discussed.
