  Anisotropic flow coefficients and their fluctuations are investigated for
Au+Au collisions at center of mass energy $\sqrt{s_{NN}}$ = 200 GeV by using a
multi-phase transport model with string melting scenario. Experimental results
of azimuthal anisotropies by means of the two- and four-particle cumulants are
generally well reproduced by the model including both parton cascade and
hadronic rescatterings. Event-by-event treatments of the harmonic flow
coefficients $v_n$ (for n = 2, 3 and 4) are performed, in which event
distributions of $v_n$ for different orders are consistent with Gaussian shapes
over all centrality bins. Systematic studies on centrality, transverse momentum
($p_{T}$) and pseudo-rapidity ($\eta$) dependencies of anisotropic flows and
quantitative estimations of the flow fluctuations are presented. The $p_{T}$
and $\eta$ dependencies of absolute fluctuations for both $v_2$ and $v_3$
follow similar trends as their flow coefficients. Relative fluctuation of
triangular flow $v_3$ is slightly centrality-dependent, which is quite
different from that of elliptic flow $v_2$. It is observed that parton cascade
has a large effect on the flow fluctuations, but hadronic scatterings make
little contribution to the flow fluctuations, which indicates flow fluctuations
are mainly modified during partonic evolution stage.
