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We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
The study of first order transition (explosive synchronization) in an ensemble (network) of coupled oscillators has been the topic of paramount interest among the researchers for more than onedecade. Several frameworks have been proposed to…
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…
Can synchronization properties of a network of identical oscillators in the presence of noise be improved through appropriate rewiring of its connections? What are the optimal network architectures for a given total number of connections?…
Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our…
Motivated by phenomena related to biological systems such as the synchronously flashing swarms of fireflies, we investigate a network of phase oscillators evolving under the generalized Kuramoto model with inertia. A distance-dependent,…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
We report finite size numerical investigations and mean field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine for a Gaussian distribution of the frequencies the transition from…
Brain networks typically exhibit characteristic synchronization patterns where several synchronized clusters coexist. On the other hand, neurological disorders are considered to be related to pathological synchronization such as excessive…
Explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. In the current work, we took into account mean-field approximations to determine the…
We explore the collective phase dynamics of Wien-bridge oscillators coupled resistively. We carefully analyze the behavior of two coupled oscillators, obtaining a transformation from voltage to effective phase. From the phase dynamics we…
Correlations between intrinsic dynamics and local topology have become a new trend in the study of synchronization in complex networks. In this paper, we investigate in this paradigm the influence of topology on dynamics of networks made up…
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…
By a model of coupled phase oscillators, we show analytically how synchronization in {\em non-identical} complex networks can be enhanced by introducing a proper gradient into the couplings. It is found that, by pointing the gradient from…
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…
Motivated by recent observations in neuronal systems we investigate all-to-all networks of non-identical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all…
We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order…
Ordered and disordered behavior in large ensembles of coupled oscillators map to different functional states in a wide range of applications, e.g., active and resting states in the brain and stable and unstable power grid configurations.…
Recent studies of dynamic properties in complex systems point out the profound impact of hidden geometry features known as simplicial complexes, which enable geometrically conditioned many-body interactions. Studies of collective behaviours…