Related papers: Nonlinear Synchronization on Connected Undirected …
The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
Sufficient conditions of consensus (synchronization) in networks described by digraphs and consisting of identical determenistic SIMO systems are derived. Identical and nonidentical control gains (positive arc weights) are considered.…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…
Synchronization in the networks of coupled oscillators is a widely studied topic in different areas. It is well-known that synchronization occurs if the connectivity of the network dominates heterogeneity of the oscillators. Despite…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators' frequencies and can…
The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multi-layered structure of connections affects the synchronization properties of dynamical systems evolving…
Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
This study investigates remote synchronization in arbitrary network clusters of coupled nonlinear oscillators, a phenomenon inspired by neural synchronization in the brain. Employing a multi-faceted approach encompassing analytical,…
Networks of coupled LC oscillators that do not share a common ground node are studied. Both resistive coupling and inductive coupling are considered. For networks under resistive coupling, it is shown that the oscillator-coupler…
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 present a general approach to the study of synchrony in networks of weakly nonlinear systems described by singularly perturbed equations of the type $x''+x+\epsilon f(x,x')=0$. By performing a perturbative calculation based on normal…