  We study an ultracold atom-cavity coupling system, which had been implemented
in experiment to display weak light nonlinearity [S. Gupta \textit{et al}.,
Phys. Rev. Lett. \textbf{99}, 213601 (2007)]. The model is described by a
non-interacting Bose-Einstein condensate contained in a Fabry-P\'{e}rot optical
resonator, in which two incommensurate standing-wave modes are excited and thus
form a quasiperiodic optical lattice potential for the atoms. Special emphasis
are paid to the variation of atomic wavefunction induced by the cavity light
field. We show that bistability between the atomic localized and extended
states can be generated under appropriate conditions.
