  We investigate the oscillatory dynamics and bifurcation structure of a
reaction-diffusion model for cell polarity formation in [Otsuji et al, PLoS
Comp. Biol. 3 (2007), e108]. We show that this model can represent formation
processes from a homogeneous initial cell to a polarized cell. The polarized
cells can be classified into three types including the type of cell polarity
oscillations. In particular, it is shown that the Turing instability can be a
trigger which eventually leads to cell polarity oscillations with the reversal
of polarity as observed in bacteria cells and melanoma cells. Moreover, we
investigate the effect of extracellular signaling on cell polarity
oscillations.
