1,622 research outputs found
Distributed Synchronization of Heterogeneous Oscillators on Networks With Arbitrary Topology
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 messages. In this paper, we study the problem of using distributed control to achieve phase and frequency synchronization of a network of coupled heterogeneous nonlinear oscillators. Not only do our controllers guarantee zero-phase error in steady state under arbitrary frequency heterogeneity, but they also require little knowledge of the oscillator nonlinearities and network topology. Furthermore, we provide a global convergence analysis, in the absence of noise and propagation delay, for the resulting nonlinear system whose phase vector evolves on the n-torus
Synchronization of Heterogeneous Kuramoto Oscillators with Arbitrary Topology
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 Positively Invariant Set (PIS) and lead to synchronization. Unlike
previous works that focus only on analytical bounds, here we introduce an
optimization approach to provide a computational-analytical bound that can
further exploit the particular features of each individual system such as
topology and frequency distribution. Examples are provided to illustrate our
results as well as the improvement over previous existing bounds
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
A chimera state is a spatio-temporal pattern in a network of identical
coupled oscillators in which synchronous and asynchronous oscillation coexist.
This state of broken symmetry, which usually coexists with a stable spatially
symmetric state, has intrigued the nonlinear dynamics community since its
discovery in the early 2000s. Recent experiments have led to increasing
interest in the origin and dynamics of these states. Here we review the history
of research on chimera states and highlight major advances in understanding
their behaviour.Comment: 26 pages, 3 figure
Control of coupled oscillator networks with application to microgrid technologies
The control of complex systems and network-coupled dynamical systems is a
topic of vital theoretical importance in mathematics and physics with a wide
range of applications in engineering and various other sciences. Motivated by
recent research into smart grid technologies we study here control of
synchronization and consider the important case of networks of coupled phase
oscillators with nonlinear interactions--a paradigmatic example that has guided
our understanding of self-organization for decades. We develop a method for
control based on identifying and stabilizing problematic oscillators, resulting
in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized
state. Interestingly, the amount of control, i.e., number of oscillators,
required to stabilize the network is primarily dictated by the coupling
strength, dynamical heterogeneity, and mean degree of the network, and depends
little on the structural heterogeneity of the network itself
Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
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 given population are heterogeneous in that their natural
frequencies are drawn from a given distribution, and each population has its
own such distribution. The coupling among the oscillators is global, however,
we permit the coupling strengths between the members of different populations
to be separately specified. We determine the critical condition for the onset
of coherent collective behavior, and develop the illustrative case in which the
oscillator frequencies are drawn from a set of (possibly different)
Cauchy-Lorentz distributions. One motivation is drawn from neurobiology, in
which the collective dynamics of several interacting populations of oscillators
(such as excitatory and inhibitory neurons and glia) are of interest.Comment: The original was replaced with a version that has been accepted to
Phys. Rev. E. The new version has the same content, but the title, abstract,
and the introductory text have been revise
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