0 1 2 3 4 −0.005 0 0.005 0.01 0.015 0.02 0.025 K$_{T}$ avg   H for Case 3 −0.00010537 −1.7297e−05 0.00048381 0.0016927 −0.00012207 8.1067e−05 0.0076261 0.015411 −0.005 0 0.005 0.01 0.015 0.02 0.025 avg   H for Case 4 Figure 13: Mean sensitivity to initial conditions for cases 3 & 4 ( M = N,L = 1 and M = 1 ,L = 0, respectively) for large networks ( N$_{T}$ = 400). Error bars indicate standard deviations. 5 Discussion In the previous section, the statistical results showed that MRBNs are more robust than classic RBNs for the same K$_{T}$ values, since modularity reduces the probability of damage to spread. This can also be confirmed analytically. The method of Luque and Sol´ e [32] can be extended to MRBNs. Instead of focussing on a single node with a Boolean state, one can focus on a single module m with internal dynamics. The probability that the internal dynamics of m may be perturbed will depend mainly on 〈 L 〉 (as well as p ). If p = 0 . 5, then L < 2 implies that on average damage will not propagate between modules, even if the internal dynamics of m are chaotic, i.e. K > 2. Still, if K >> 2, i.e. m is deep within the chaotic phase because of a high number of intramodular links, then the fragility of the network will be noticeable in the MRBN (Δ H >> 0) even if damage does not spread outside m . It is clear that damage spreading will depend on the value of K as well, e.g. if K is small, damage will have a lower probability of propagating within modules, affecting the probability of spread across modules. Since damage across the whole MRBN can spread through internal ( K ) or external ( L ) links, it can be seen that there is the following relationship between critical L and K , extending equation 1: 〈 L$_{c}$ 〉 〈 K$_{c}$ 〉 = 1 2 p (1 − p ) (13) 22