  We study the dynamics of the Internet topology based on the empirical data on
the level of the autonomous systems. It is found that the fluctuations
occurring in the stochastic process of connecting and disconnecting edges are
important features of the Internet dynamics. The network's overall growth can
be described approximately by a single characteristic degree growth rate
$g_{\rm eff} \approx 0.016$ and the fluctuation strength $\sigma_{\rm eff}
\approx 0.14$, together with the vertex growth rate $\alpha \approx 0.029$. A
stochastic model which incorporate these values and an adaptation rule newly
introduced reproduces several features of the real Internet topology such as
the correlations between the degrees of different vertices.
