  In this paper we study the effect of external harmonic forcing on a
one-dimensional oscillatory system described by the complex Ginzburg-Landau
equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous
state with no spatial structure is observed. The state becomes unstable to a
spatially periodic ``stripe'' state via a supercritical bifurcation as the
forcing amplitude decreases. An approximate phase equation is derived, and an
analytic solution for the stripe state is obtained, through which the
asymmetric behavior of the stability border of the state is explained. The
phase equation, in particular the analytic solution, is found to be very useful
in understanding the stability borders of the homogeneous and stripe states of
the forced CGLE.

Statistical Mechanics;Pattern Formation and Solitons