Related papers: Threshold graphs are globally synchronizing
Higher-order networks with multiway interactions can exhibit collective dynamical phenomena that are absent in traditional pairwise network models. However, analyzing such dynamics becomes computationally prohibitive as their state space…
We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic…
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
We establish thresholds for the feasibility of random multi-graph alignment in two models. In the Gaussian model, we demonstrate an "all-or-nothing" phenomenon: above a critical threshold, exact alignment is achievable with high…
Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
When two graphs have a correlated Bernoulli distribution, we prove that the alignment strength of their natural bijection strongly converges to a novel measure of graph correlation $\rho_T$ that neatly combines intergraph with intragraph…
In this work, a novel approach for the reliable and efficient numerical integration of the Kuramoto model on graphs is studied. For this purpose, the notion of order parameters is revisited for the classical Kuramoto model describing…
We investigate transition to synchronization in Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage ($f$) of higher degree nodes of the network are assumed to be…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
The purpose of this paper is to highlight the role played by the anti-regular graph within the class of threshold graphs. Using the fact that every threshold graph contains a maximal anti-regular graph, we show that some known results, and…
The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models…
We show that by restricting the degrees of the vertices of a graph to an arbitrary set \( \Delta \), the threshold point $ \alpha(\Delta) $ of the phase transition for a random graph with $ n $ vertices and $ m = \alpha(\Delta) n $ edges…
Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted operator that rescales each edge according to how far its…
Synchronization in networks of interconnected oscillators is a fascinating phenomenon that appear naturally in many independent fields of science and engineering. A substantial amount of work has been devoted to understanding all possible…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
We consider the synchronization problem of swing equations, a second-order Kuramoto-type model, on connected networks with inhomogeneous dampings. This was largely motivated by its relevance to the dynamics of power grids. We focus on the…
Random geometric graphs result from taking $n$ uniformly distributed points in the unit cube, $[0,1]^d$, and connecting two points if their Euclidean distance is at most $r$, for some prescribed $r$. We show that monotone properties for…
We show that the degree distributions of graphs do not suffice to characterize the synchronization of systems evolving on them. We prove that, for any given degree sequence satisfying certain conditions, there exists a connected graph…