A bifurcation analysis of dune shape transition is made. By use of a reduced
model of dune morphodynamics, dune skeleton model, we elucidate the transition
mechanism between different shapes of dunes under unidirectional wind. It was
found that the decrease in the total amount of sand in the system and/or the
lateral sand flow shifts the stable state from a straight transverse dune to
wavy transverse dune through a pitchfork bifurcation. A further decrease causes
wavy transverse dunes to shift into barchans through a Hopf bifurcation. These
bifurcation structures reveal the transition mechanism of dune shapes under
unidirectional wind