Related papers: Modular synchronization in complex networks with a…
Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
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…
We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
In this work we investigate the stability of synchronized states for the Kuramoto model on scale-free and random networks in the presence of white noise forcing. We show that for a fixed coupling constant, the robustness of the globally…
We introduce the concept of synchronization bombs as large networks of coupled heterogeneous oscillators that operate in a bistable regime and abruptly transit from incoherence to phase-locking (or vice-versa) by adding (or removing) one or…
Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics,…
While shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network,the suppressing tendency of the heterogeneity of the degree distribution, even for…
We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation…
Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise…
We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive…
In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a…
Synchronization processes are ubiquitous despite the many connectivity patterns that complex systems can show. Usually, the emergence of synchrony is a macroscopic observable, however, the microscopic details of the system, as e.g. the…
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…
The Kuramoto-Sakaguchi model for coupled phase oscillators with phase-frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture…
In this paper, we study the discrete-time consensus problem over networks with antagonistic and cooperative interactions. Following the work by Altafini [IEEE Trans. Automatic Control, 58 (2013), pp. 935--946], by an antagonistic…
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…
Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal…
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…