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We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the…

We study networks of coupled bistable elastic elements, recently proposed as a model for crumpled thin sheets. The networks are poised on the verge of a localized instability, and the model allows unique access to both local and global…

We study the coevolutionary dynamics of network topology and social complex contagion using a threshold cascade model. Our coevolving threshold model incorporates two mechanisms: the threshold mechanism for the spreading of a minority state…

Precipitation is one of the most important meteorological variables for defining the climate dynamics, but the spatial patterns of precipitation have not been fully investigated yet. The complex network theory, which provides a robust tool…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what…

The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…

Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…

We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary…

In nature, barchan dunes typically exist as members of larger fields that display striking, enigmatic structures that cannot be readily explained by examining the dynamics at the scale of single dunes, or by appealing to patterns in…

The Abelian sandpile model serves as a canonical example of self-organized criticality. This critical behavior manifests itself through large cascading events triggered by small perturbations. Such large-scale events, known as avalanches,…

Interdependencies are ubiquitous throughout the world. Every real-world system interacts with and is dependent on other systems, and this interdependency affects their performance. In particular, interdependencies among networks make them…

Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour: These avalanches are characterized by a power law distribution for the size and…

For large-scale power networks, the failure of particular transmission lines can offload power to other lines and cause self-protection trips to activate, instigating a cascade of line failures. In extreme cases, this can bring down the…

The aim of this study is to investigate a wave dynamics and size scaling of avalanches which were created by the mathematical model {[}J. \v{C}ern\'ak Phys. Rev. E \textbf{65}, 046141 (2002)]. Numerical simulations were carried out on a two…

This paper considers the dynamics of edges in a network. The Dynamic Bond Percolation (DBP) process models, through stochastic local rules, the dependence of an edge $(a,b)$ in a network on the states of its neighboring edges. Unlike…

We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…

Power generation and distribution remains an important topic of discussion since the industrial revolution. As the system continues to grow, it needs to evolve both in infrastructure, robustness and its resilience to deal with failures. One…

Analyzing the behavior of complex interdependent networks requires complete information about the network topology and the interdependent links across networks. For many applications such as critical infrastructure systems, understanding…

We use observed transmission line outage data to make a Markov influence graph that describes the probabilities of transitions between generations of cascading line outages, where each generation of a cascade consists of a single line…