3,295 research outputs found
Dynamically-Coupled Oscillators -- Cooperative Behavior via Dynamical Interaction --
We propose a theoretical framework to study the cooperative behavior of
dynamically coupled oscillators (DCOs) that possess dynamical interactions.
Then, to understand synchronization phenomena in networks of interneurons which
possess inhibitory interactions, we propose a DCO model with dynamics of
interactions that tend to cause 180-degree phase lags. Employing an approach
developed here, we demonstrate that although our model displays synchronization
at high frequencies, it does not exhibit synchronization at low frequencies
because this dynamical interaction does not cause a phase lag sufficiently
large to cancel the effect of the inhibition. We interpret the disappearance of
synchronization in our model with decreasing frequency as describing the
breakdown of synchronization in the interneuron network of the CA1 area below
the critical frequency of 20 Hz.Comment: 10 pages, 3 figure
Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation
We present a detailed study of the effect of time delay on the collective
dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple
model consisting of just two oscillators with a time delayed coupling, the
bifurcation diagram obtained by numerical and analytical solutions shows
significant changes in the stability boundaries of the amplitude death, phase
locked and incoherent regions. A novel result is the occurrence of amplitude
death even in the absence of a frequency mismatch between the two oscillators.
Similar results are obtained for an array of N oscillators with a delayed mean
field coupling and the regions of such amplitude death in the parameter space
of the coupling strength and time delay are quantified. Some general analytic
results for the N tending to infinity (thermodynamic) limit are also obtained
and the implications of the time delay effects for physical applications are
discussed.Comment: 20 aps formatted revtex pages (including 13 PS figures); Minor
changes over the previous version; To be published in Physica
Synchronization of Coupled Nonidentical Genetic Oscillators
The study on the collective dynamics of synchronization among genetic
oscillators is essential for the understanding of the rhythmic phenomena of
living organisms at both molecular and cellular levels. Genetic oscillators are
biochemical networks, which can generally be modelled as nonlinear dynamic
systems. We show in this paper that many genetic oscillators can be transformed
into Lur'e form by exploiting the special structure of biological systems. By
using control theory approach, we provide a theoretical method for analyzing
the synchronization of coupled nonidentical genetic oscillators. Sufficient
conditions for the synchronization as well as the estimation of the bound of
the synchronization error are also obtained. To demonstrate the effectiveness
of our theoretical results, a population of genetic oscillators based on the
Goodwin model are adopted as numerical examples.Comment: 16 pages, 3 figure
Synchronization in dynamical networks of locally coupled self-propelled oscillators
Systems of mobile physical entities exchanging information with their
neighborhood can be found in many different situations. The understanding of
their emergent cooperative behaviour has become an important issue across
disciplines, requiring a general conceptual framework in order to harvest the
potential of these systems. We study the synchronization of coupled oscillators
in time-evolving networks defined by the positions of self-propelled agents
interacting in real space. In order to understand the impact of mobility in the
synchronization process on general grounds, we introduce a simple model of
self-propelled hard disks performing persistent random walks in 2 space and
carrying an internal Kuramoto phase oscillator. For non-interacting particles,
self-propulsion accelerates synchronization. The competition between agent
mobility and excluded volume interactions gives rise to a richer scenario,
leading to an optimal self-propulsion speed. We identify two extreme dynamic
regimes where synchronization can be understood from theoretical
considerations. A systematic analysis of our model quantifies the departure
from the latter ideal situations and characterizes the different mechanisms
leading the evolution of the system. We show that the synchronization of
locally coupled mobile oscillators generically proceeds through coarsening
verifying dynamic scaling and sharing strong similarities with the phase
ordering dynamics of the 2 XY model following a quench. Our results shed
light into the generic mechanisms leading the synchronization of mobile agents,
providing a efficient way to understand more complex or specific situations
involving time-dependent networks where synchronization, mobility and excluded
volume are at play
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
Hopf normal form with symmetry and reduction to systems of nonlinearly coupled phase oscillators
Coupled oscillator models where oscillators are identical and
symmetrically coupled to all others with full permutation symmetry are
found in a variety of applications. Much, but not all, work on phase
descriptions of such systems consider the special case of pairwise coupling
between oscillators. In this paper, we show this is restrictive - and we
characterise generic multi-way interactions between oscillators that are
typically present, except at the very lowest order near a Hopf bifurcation
where the oscillations emerge. We examine a network of identical weakly coupled
dynamical systems that are close to a supercritical Hopf bifurcation by
considering two parameters, (the strength of coupling) and
(an unfolding parameter for the Hopf bifurcation). For small enough
there is an attractor that is the product of stable limit cycles; this
persists as a normally hyperbolic invariant torus for sufficiently small
. Using equivariant normal form theory, we derive a generic normal
form for a system of coupled phase oscillators with symmetry. For fixed
and taking the limit , we show that the
attracting dynamics of the system on the torus can be well approximated by a
coupled phase oscillator system that, to lowest order, is the well-known
Kuramoto-Sakaguchi system of coupled oscillators. The next order of
approximation genericlly includes terms with up to four interacting phases,
regardless of . Using a normalization that maintains nontrivial interactions
in the limit , we show that the additional terms can lead
to new phenomena in terms of coexistence of two-cluster states with the same
phase difference but different cluster size
Uniform synchronous criticality of diversely random complex networks
We investigate collective synchronous behaviors in random complex networks of
limit-cycle oscillators with the non-identical asymmetric coupling scheme, and
find a uniform coupling criticality of collective synchronization which is
independent of complexity of network topologies. Numerically simulations on
categories of random complex networks have verified this conclusion.Comment: 8 pages, 4 figure
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