  We propose a simple mathematical model that describes the time evolution of a
self-propelled object on a liquid surface using such variables as the object
location, the surface concentration of active molecules and the hydrodynamic
surface flow. The model is applied to simulate the time evolution of a rotor
composed of a polygonal plate with camphor pills at its corners. We have
qualitatively reproduced results of experiments, in which the inversion of
rotational direction under periodic stop-and-release operations was
investigated. The model correctly describes the probability of the inversion as
a function of the duration of the phase when the rotor is stopped. Moreover,
the model allows to introduce the rotor asymmetry unavoidable in real
experiments and study its influence on the studied phenomenon. Our numerical
simulations have revealed that the probability of the inversion of rotational
direction is determined by the competition among the transport of the camphor
molecules by the flow, the intrinsic asymmetry of the rotor, and the noise
amplitude.
