Related papers: Avoiding catastrophic failure in correlated networ…
Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
With the development of neural networks based machine learning and their usage in mission critical applications, voices are rising against the \textit{black box} aspect of neural networks as it becomes crucial to understand their limits and…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
Recent research has identified interactions between networks as crucial for the outcome of evolutionary games taking place on them. While the consensus is that interdependence does promote cooperation by means of organizational complexity…
A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have…
Many complex networks display remarkable resilience under external perturbations, internal failures and environmental changes, yet they can swiftly deteriorate into dysfunction upon the removal of a few keystone nodes. Discovering theories…
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…
Network's resilience to the malfunction of its components has been of great concern. The goal of this work is to determine the network design guidelines, which maximizes the network efficiency while keeping the cost of the network (that is…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
A central issue in complex networks is tolerance to random failures and intentional attacks. Current literature emphasizes the dichotomy between networks with a power-law node connectivity distribution, which are robust to random failures…
Networks are useful descriptions of the structure of many complex systems. Unsurprisingly, it is thus important to analyze the robustness of networks in many scientific disciplines. In applications in communication, logistics, finance,…
Modern world builds on the resilience of interdependent infrastructures characterized as complex networks. Recently, a framework for analysis of interdependent networks has been developed to explain the mechanism of resilience in…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…