Cascading failures in interdependent networks have been investigated recently using percolation theory. Here, we study the microscopic dynamics of the cascading failures. For simplicity, we analyze a system composed of a pair of fully interdependent Erdös-Rényi (ER) networks [1]. We show that the cascading process for single random realizations cannot be predicted by mean field theory for p (fraction of unremoved nodes) close to p_c. We study the scaling behavior of the total number of cascades, τ, as a function of the number of nodes N and p. We find that when p is chosen as the average p_c over all realizations, the mean time <τ>~N^1/4 [1]. However, if p is chosen as the real p_c for each realization, we obtain that <τ>~N^1/3. This new scaling result can be well understood by a critical percolation process that occurs during the cascading failures at p_c. We also reveal the theoretical relationship between these two scaling results.

[1] S. V. Buldyrev et al., Nature 464, 1025 (2010).