Related papers: Shock waves on complex networks

We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…

Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach…

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…

We introduce a probabilistic framework that represents stylized banking networks with the aim of predicting the size of contagion events. Most previous work on random financial networks assumes independent connections between banks, whereas…

In this paper, we study information cascades on graphs. In this setting, each node in the graph represents a person. One after another, each person has to take a decision based on a private signal as well as the decisions made by earlier…

Much work has been devoted to studying percolation of networks and interdependent networks under varying levels of failures. Researchers have considered many different realistic network structures, but thus far no study has incorporated the…

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…

Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we…

Many critical infrastructure systems have network structure and are under stress. Despite their national importance, the complexity of large-scale transport networks means we do not fully understand their vulnerabilities to cascade…

This paper discusses first passage percolation and flooding on large weighted sparse random graphs with two types of nodes: active and passive nodes. In mathematical physics passive nodes can be interpreted as closed gates where fluid flow…

Physical infrastructure systems supply crucial resources to residential, commercial, and industrial activities. These infrastructure systems generally consist of multiple types of infrastructure assets that are interdependent. In the event…

We probe the stability of Watts-Strogatz DC microgrids, in which droop-controlled producers and constant power load consumers are homogeneously distributed and obey Kirchhoff's circuit laws. The concept of survivability is employed to…

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamics and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A…

Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet, they are disregarded in standard analytic methods as…

We study static nonlinear waves in networks described by a nonlinear Schrodinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boundary conditions are obtained. Spontaneous symmetry breaking…

This paper develops a mathematical framework to study signal networks, in which nodes can be active or inactive, and their activation or deactivation is driven by external signals and the states of the nodes to which they are connected via…

We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal…

We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we…

Recent studies of attacks on complex networks suggest that small initial breakdowns can lead to global cascades of overload failures in communication, economic trading, and supply-transportation systems, considering the defense methods is…

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…