Related papers: The Kuramoto model on dynamic random graphs
We study the dynamics of a generalized version of the famous Kuramoto-Sakaguchi coupled oscillator model. In the classic version of this system, all oscillators are governed by the same ODE, which depends on the order parameter of the…
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…
Networks of coupled oscillators are some of the most studied objects in the theory of dynamical systems. Two important areas of current interest are the study of synchrony in highly disordered systems and the modeling of systems with…
We study a system of coupled oscillators of the Sakaguchi-Kuramoto type with interactions including a phase delay. We consider the case of a coupling matrix such that oscillators with large natural frequencies drive all slower ones but not…
We propose a generalized Kuramoto model with relativistic effects and investigate emergent asymptotic behaviors. The proposed generalized Kuramoto model incorporates relativistic Kuramoto(RK) type models which can be derived from the…
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…
Consider $n$ identical Kuramoto oscillators on a random graph. Specifically, consider \ER random graphs in which any two oscillators are bidirectionally coupled with unit strength, independently and at random, with probability $0\leq p\leq…
Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines,…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…
We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is…
Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that…
We study the influence of motion on the emergence of synchronization in a metapopulation of random walkers moving on a heterogeneous network and subject to Kuramoto interactions at the network nodes. We discover a novel mechanism of…
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such…
The multidimensional Kuramoto model describes the synchronization dynamics of particles moving on the surface of D-dimensional spheres, generalizing the original model where particles were characterized by a single phase. In this setup,…
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…
The Kuramoto model has been introduced to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. The model consists of $N$ interacting oscillators on the one dimensional sphere $\mathbf{S}^{1}$, driven…
In a large variety of systems (biological, physical, social etc.), synchronization occurs when different oscillating objects tune their rhythm when they interact with each other. The different underlying network defining the connectivity…