  This paper is devoted to the study of the asymptotic dynamics of the
stochastic damped sine-Gordon equation with homogeneous Neumann boundary
condition. It is shown that for any positive damping and diffusion
coefficients, the equation possesses a random attractor, and when the damping
and diffusion coefficients are sufficiently large, the random attractor is a
one-dimensional random horizontal curve regardless of the strength of noise.
Hence its dynamics is not chaotic. It is also shown that the equation has a
rotation number provided that the damping and diffusion coefficients are
sufficiently large, which implies that the solutions tend to oscillate with the
same frequency eventually and the so called frequency locking is successful.
