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We study under which conditions systems of coupled oscillators on complex networks display remote synchronization, a situation where pairs of vertices, not necessarily physically linked, but with the same network symmetry, are synchronized.
We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained…
Synchronization control of coupled continuous-time linear systems is studied. For identical systems that are stabilizable, a linear feedback law obtained via algebraic Riccati equation is shown to synchronize any fixed directed network of…
The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
We study synchronization phenomenon in a self-correcting population of noisy phase oscillators with randomly distributed natural frequencies. In our model each oscillator stochastically switches its phase to the ensemble-averaged value…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units.…
Synchronization systems with effective inertia, such as power grid networks and coupled electromechanical oscillators, are commonly modeled by the second-order Kuramoto model. In the forward process, numerical simulations exhibit a…
This brief paper further investigates the locally and globally adaptive synchronization of an uncertain complex dynamical network. Several network synchronization criteria are deduced. Especially, our hypotheses and designed adaptive…
We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted…
Synchronization, the emergence of spontaneous order in coupled systems, is of fundamental importance in both physical and biological systems. We demonstrate the synchronization of two dissimilar silicon nitride micromechanical oscillators,…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
We introduce a system of pulse coupled oscillators that can change both their phases and frequencies; and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on…
Clock synchronization is ubiquitous in wireless systems for communication, sensing and control. In this paper we design a scalable system in which an indefinite number of passively receiving wireless units can synchronize to a single master…
We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance in power-grids where energy is either…
In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and…
In this paper, we consider the synchronization of heterogeneous pulse-coupled oscillators (PCOs), where some of the oscillators might be faulty or malicious. The oscillators interact through identical pulses at discrete instants and evolve…