  A model of an autonomous three-sphere microswimmer is proposed by
implementing a coupling effect between the two natural lengths of an elastic
microswimmer. Such a coupling mechanism is motivated by the previous models for
synchronization phenomena in coupled oscillator systems. We numerically show
that a microswimmer can acquire a nonzero steady state velocity and a finite
phase difference between the oscillations in the natural lengths. These
velocity and phase difference are almost independent of the initial phase
difference. There is a finite range of the coupling parameter for which a
microswimmer can have an autonomous directed motion. The stability of the phase
difference is investigated both numerically and analytically in order to
determine its bifurcation structure.
