Related papers: Simultaneous first and second order percolation tr…
We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on the nodes of network B and a fraction of the nodes in network B depends on the nodes of network A. Due to the…
The collapse of interdependent networks, as well as similar avalanche phenomena, is driven by cascading failures. At the critical point, the cascade begins as a critical branching process, where each failing node (element) triggers, on…
Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…
We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an…
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…
Phase transitions are fundamental features of statistical physics. While the well-studied continuous phase transitions are known to be controlled by external \textit{macroscopic} changes in the order parameter, the origin of abrupt…
We present a cascading failure model of two interdependent networks in which functional nodes belong to components of size greater than or equal to $s$. We find theoretically and via simulation that in complex networks with random…
It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and hence system-wide disasters. A recent model shows how pairs of interdependent networks can exhibit an…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our…
The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for increasing range of dependency couplings, different types of…
We study a problem of failure of two interdependent networks in the case of correlated degrees of mutually dependent nodes. We assume that both networks (A and B) have the same number of nodes $N$ connected by the bidirectional dependency…
Many man-made networks support each other to provide efficient services and resources to the customers, despite that this support produces a strong interdependency between the individual networks. Thus an initial failure of a fraction $1-p$…
While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered…
The functionality of an entity frequently necessitates the support of a group situated in another layer of the system. To unravel the profound impact of such group support on a system's resilience against cascading failures, we devise a…
Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show…
We study the cascading failures in a system composed of two interdependent square lattice networks A and B placed on the same Cartesian plane, where each node in network A depends on a node in network B randomly chosen within a certain…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…
Many systems, ranging from engineering to medical to societal, can only be properly characterized by multiple interdependent networks whose normal functioning depends on one another. Failure of a fraction of nodes in one network may lead to…