Related papers: A minimal model of partial synchrony
The Kuramoto model serves as a paradigm to study the phenomenon of spontaneous collective synchronization. We study here a nontrivial generalization of the Kuramoto model by including an interaction that breaks explicitly the rotational…
We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…
We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures…
We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
Coupled oscillators can serve as a testbed for larger questions of pattern formation across many areas of science and engineering. Much effort has been dedicated to the Kuramoto model and phase oscillators, but less has focused on…
Finite-size effects in the Kuramoto model are known to induce collective fluctuations even below the critical coupling, where the thermodynamic limit predicts complete asynchrony. While the shot-noise approach developed in our recent work…
The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto…
We consider ensembles of sine-coupled phase oscillators consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble…
The Kuramoto model, a paradigmatic framework for studying synchronization, exhibits a transition to collective oscillations only above a critical coupling strength in the thermodynamic limit. However, real-world systems are finite, and…
The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…
Synchronization in a frequency-weighted Kuramoto model with a uniform frequency distribution is studied. We plot the bifurcation diagram and identify the asymptotic coherent states. Numerical simulations show that the system undergoes two…
We investigate the engineering scenario where the objective is to synchronize heterogeneous oscillators in a distributed fashion. The internal dynamics of each oscillator are general enough to capture their time-varying natural frequency as…
Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…
This review offers a retrospective of the development of the theory of coupled oscillators and synchronization over the past half century. Among the various works made by myself during this period, the following three specific works will be…
Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto…
Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
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…
Synchronisation of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics, to social networks and technology. A fundamental and long-time goal in the study of synchronisation has been to find…