相关论文: Critical phenomena in complex networks

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…

Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…

Modern network-like systems are usually coupled in such a way that failures in one network can affect the entire system. In infrastructures, biology, sociology, and economy, systems are interconnected and events taking place in one system…

Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…

The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…

In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organized criticality, a specific type of non-equilibrium…

A simple model of the driven motion of interacting particles in a two dimensional random medium is analyzed, focusing on the critical behavior near to the threshold that separates a static phase from a flowing phase with a steady-state…

The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and…

Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…

Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…

We develop the theory of the k-core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the k-core percolation is an unusual, hybrid phase transition with a jump emergence of the k-core…

When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…

Networks are structures that pervade many natural and man-made phenomena. Recent findings have characterized many networks as not random structures, but as efficent complex formations. Current research has examined complex networks as…

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 theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…

Percolation theory has been widely used to study phase transitions in complex networked systems. It has also successfully explained several macroscopic phenomena across different fields. Yet, the existent theoretical framework for…

We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…

In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…

Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…