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We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of…
In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems…
Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's…
A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes…
Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
This paper studies synchronization in coupled nonlinear dynamic networks with unknown parameters. Adaptation can be added to one or several elements in the network, while preserving the global synchronization conditions derived in…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
A networked oscillator based analysis is performed for periodic bluff body flows to examine and control the transfer of kinetic energy. Spatial modes extracted from the flow field with corresponding amplitudes form a set of oscillators…
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…
Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition, and…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
We have investigated synchronized pattern in a network of Thomas oscillators coupled with sinusoidal nonlinear coupling. Pattern like chimera states are not only observed for many non-locally coupled oscillators but there is a signature of…
Functional brain networks can change rapidly as a function of stimuli or cognitive shifts. Tracking dynamic functional connectivity is particularly challenging as it requires estimating the structure of the network at each moment as well as…
We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected…
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…
We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…