Related papers: Complex dynamics in adaptive phase oscillator netw…
In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random…
We study the phase synchronization of Kuramoto's oscillators in small parts of networks known as motifs. We first report on the system dynamics for the case of a scale-free network and show the existence of a non-trivial critical point. We…
Partial, instead of complete, synchronization has been widely observed in various networks including, in particular, brain networks. Motivated by data from human brain functional networks, in this technical note, we analytically show that…
We study the emergent collective behaviors for an ensemble of identical Kuramoto oscillators under the effect of inertia. In the absence of inertial effects, it is well known that the generic initial Kuramoto ensemble relaxes to the…
We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row(or column)-summable network topology, we show…
The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study a wide range of systems. Despite numerous efforts to…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
The slowing of Moore's law and the increasing energy demands of machine learning present critical challenges for both the hardware and machine learning communities, and drive the development of novel computing paradigms. Of particular…
The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators…
We investigate the interplay between phase lag and adaptive learning rules in a network of identical pendulum oscillators, where the coupling strengths evolve dynamically in response to the oscillators' states. Specifically, we examine two…
We present a framework for controlling the collective phase of a system of coupled oscillators described by the Kuramoto model under the influence of a periodic external input by combining the methods of dynamical reduction and optimal…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
Previous results have shown that a large class of complex systems consisting of many interacting heterogeneous phase oscillators exhibit an attracting invariant manifold. This result has enabled reduced analytic system descriptions from…
Most real-world networks exhibit a significant degree of modularity. Understanding the effects of such topology on dynamical processes is pivotal for advances in social and natural sciences. In this work we consider the dynamics of Kuramoto…
Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension…
A small-world network (SW) of similar phase oscillators, interacting according to the Kuramoto model is studied numerically. It is shown that deterministic Kuramoto dynamics on the SW networks has various stable stationary states. This can…
The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the…