Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional throughout the cascade. Although suitable for communication networks, this assumption fails to capture the dependencies in systems carrying a flow (e.g., power systems, road transportation networks), where cascading failures are often triggered by redistribution of flows leading to overloading of lines. Here, we consider a model consisting of systems $A$ and $B$ with initial line loads and capacities given by ${\{L_{A,i},C_{A,i}\}}_{i=1}^n$ and ${\{L_{B,i},C_{B,i}\}}_{i=1}^n$, respectively. When a line fails in system $A$, $a$ fraction of its load is redistributed to alive lines in $B$, while remaining $(1-a)$ fraction is redistributed equally among all functional lines in $A$; a line failure in $B$ is treated similarly with $b$ giving the fraction to be redistributed to $A$. We give a thorough analysis of cascading failures of this model initiated by a random attack targeting $p_1$ fraction of lines in $A$ and $p_2$ fraction in $B$. We show that (i) the model captures the real-world phenomenon of unexpected large scale cascades and exhibits interesting transition behavior: the final collapse is always first order, but it can be preceded by a sequence of first- and second-order transitions; (ii) network robustness tightly depends on the coupling coefficients $a$ and $b$, and robustness is maximized at non-trivial $a,b$ values in general; (iii) unlike most existing models, interdependence has a multifaceted impact on system robustness in that interdependency can lead to an improved robustness for each individual network.

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• Cascades
• Continuous phase transition
• Discontinuous phase transition
• Network resilience
• Robustness