Related papers: A Universal Route to Explosive Phenomena

We discuss several interesting random network models which exhibit (provable) explosive transitions and their applications.

Spatially extended chaotic systems with power-law decaying interactions are considered. Two coupled replicas of such systems synchronize to a common spatio-temporal chaotic state above a certain coupling strength. The synchronization…

Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rhythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards…

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…

The Kuramoto model of a network of coupled phase oscillators exhibits a first-order phase transition when the distribution of natural frequencies has a finite flat region at its maximum. First-order phase transitions including hysteresis…

This study investigates how visibility graphs constructed from Monte Carlo Markov Chain time series of spin models capture the critical behavior of the system. More precisely, we show that this approach identifies continuous phase…

Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order…

Population bursts in a large ensemble of coupled elements result from the interplay between the local excitable properties of the nodes and the global network topology. Here collective excitability and self-sustained bursting oscillations…

Excited-state quantum phase transitions (ESQPTs) are critical phenomena that generate singularities in the spectrum of quantum systems. {For systems with a classical counterpart,} these phenomena have their origin in the classical limit…

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…

Ecological systems, as is often noted, are complex. Equally notable is the generalization that complex systems tend to be oscillatory, whether Huygens simple patterns of pendulum entrainment or the twisted chaotic orbits of Lorenz…

We study an interacting particle system in which moving particles activate dormant particles linked by the components of critical bond percolation. Addressing a conjecture from Beckman, Dinan, Durrett, Huo, and Junge for a continuous…

Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for…

We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase…

We introduce a condition for an ensemble of networked phase oscillators to feature an abrupt, first-order phase transition from an unsynchronized to a synchronized state. This condition is met in a very wide spectrum of situations, and for…

Changing the interactions between particles in an ensemble-by varying the temperature or pressure, for example-can lead to phase transitions whose critical behaviour depends on the collective nature of the many-body system. Despite the…

The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…

Some models allowing explicit calculation of periodic instantons and evaluation of their action are studied with regard to transitions from classical to quantum behaviour as the temperature is lowered and tunneling sets in. It is shown that…

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same…