Related papers: A Universal Route to Explosive Phenomena
The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter, we demonstrate that the nodes in a second-order Kuramoto model, perform a cascade…
Yet often neglected, dynamical interdependencies between concomitant contagion processes can alter their intrinsic equilibria and bifurcations. A particular case of interest for disease control is the emergence of explosive transitions in…
Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…
Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…
The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks. Thus, there is great interest in analyzing phase transitions to large-scale…
Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the…
Explosive Percolation describes the abrupt onset of large-scale connectivity that results from a simple random process designed to delay the onset of the transition on an underlying random network or lattice. Explosive percolation…
Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature yet characterising the transition that gives rise to it has remained an elusive task. Although in recent studies critical points marking the onset of…
Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…
This study aims to develop a generalised concept that will enable double explosive transitions in the forward and backward directions or a combination thereof. We found two essential factors for generating such phase transitions: the use of…
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…
Dynamics of complex systems are often driven by interactions that extend beyond pairwise links, underscoring the need to establish a correspondence between interpretable system parameters and emergent phenomena in hypergraph-based networks.…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
We explore synchronization transitions in even-$D$-dimensional generalized Kuramoto oscillators on both complete graphs and $d$-dimensional lattices. In the globally coupled system, analytical expansions of the self-consistency equations,…
The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make…
We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
Synchronization commonly occurs in many natural and man-made systems, from neurons in the brain to cardiac cells to power grids to Josephson junction arrays. Transitions to or out of synchrony for coupled oscillators depend on several…
Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as $k$-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Much effort has…