ﻻ يوجد ملخص باللغة العربية
Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this critical dependency (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.
We propose a novel algorithm that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential(ability) which is updated during the tournament acc
Cascading failures constitute an important vulnerability of interconnected systems. Here we focus on the study of such failures on networks in which the connectivity of nodes is constrained by geographical distance. Specifically, we use random geomet
Many real world complex systems such as infrastructure, communication and transportation networks are embedded in space, where entities of one system may depend on entities of other systems. These systems are subject to geographically localized failu
Computer viruses are evolving by developing spreading mechanisms based on the use of multiple vectors of propagation. The use of the social network as an extra vector of attack to penetrate the security measures in IP networks is improving the effect
In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may as well play an important role, resulting in a complex interplay between to