Figure 4 | Scientific Reports

Figure 4

From: Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds

Figure 4

Order parameters for the “mass rule”, for a system of networks with internal distribution P A (k) = P B (k) = δ k,5, supply distributions P sA (k) = P sB (k) = δ k,2 and thresholds k A * = k B * = 1. All the components of size h = 1 are deleted (q(1) = 1), and all the components of size h ≥ 3 are preserved (q(3) = q(4) = ... = q(h max ) = 0 where h max is the maximum value of h). The curves represent the case q(2) = 0.3 (, ), for which there is a continuous transition, and q(2) = 0.85 (, ), which leads to an abrupt breakdown of the order parameter. The dashed lines represent the theoretical results and the symbols the stochastic simulations. (a) Network A, (b) Network B.

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