306 research outputs found
The Spectrum of the Partially Locked State for the Kuramoto Model
We solve a longstanding stability problem for the Kuramoto model of coupled
oscillators. This system has attracted mathematical attention, in part because
of its applications in fields ranging from neuroscience to condensed-matter
physics, and also because it provides a beautiful connection between nonlinear
dynamics and statistical mechanics. The model consists of a large population of
phase oscillators with all-to-all sinusoidal coupling. The oscillators'
intrinsic frequencies are randomly distributed across the population according
to a prescribed probability density, here taken to be unimodal and symmetric
about its mean. As the coupling between the oscillators is increased, the
system spontaneously synchronizes: the oscillators near the center of the
frequency distribution lock their phases together and run at the same
frequency, while those in the tails remain unlocked and drift at different
frequencies. Although this ``partially locked'' state has been observed in
simulations for decades, its stability has never been analyzed mathematically.
Part of the difficulty is in formulating a reasonable infinite-N limit of the
model. Here we describe such a continuum limit, and prove that the
corresponding partially locked state is, in fact, neutrally stable, contrary to
what one might have expected. The possible implications of this result are
discussed
Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons
We explore the dynamics of an integrate-and-fire neuron with an oscillatory
stimulus. The frustration due to the competition between the neuron's natural
firing period and that of the oscillatory rhythm, leads to a rich structure of
asymptotic phase locking patterns and ordering dynamics. The phase transitions
between these states can be classified as either tangent or discontinuous
bifurcations, each with its own characteristic scaling laws. The discontinuous
bifurcations exhibit a new kind of phase transition that may be viewed as
intermediate between continuous and first order, while tangent bifurcations
behave like continuous transitions with a diverging coherence scale.Comment: 4 pages, 5 figure
An Inter-Networking Mechanism with Stepwise Synchronization for Wireless Sensor Networks
To realize the ambient information society, multiple wireless networks deployed in the region and devices carried by users are required to cooperate with each other. Since duty cycles and operational frequencies are different among networks, we need a mechanism to allow networks to efficiently exchange messages. For this purpose, we propose a novel inter-networking mechanism where two networks are synchronized with each other in a moderate manner, which we call stepwise synchronization. With our proposal, to bridge the gap between intrinsic operational frequencies, nodes near the border of networks adjust their operational frequencies in a stepwise fashion based on the pulse-coupled oscillator model as a fundamental theory of synchronization. Through simulation experiments, we show that the communication delay and the energy consumption of border nodes are reduced, which enables wireless sensor networks to communicate longer with each other
Physics of the rhythmic applause
We discuss in detail a human scale example of the synchronization phenomenon,
namely the dynamics of the rhythmic applause. After a detailed experimental
investigation, we describe the phenomenon with an approach based on the
classical Kuramoto model. Computer simulations based on the theoretical
assumptions, reproduce perfectly the observed dynamics. We argue that a
frustration present in the system is responsible for the interesting interplay
between synchronized and unsynchronized regimesComment: 5 pages, 5 figure
Spatial patterns of desynchronization bursts in networks
We adapt a previous model and analysis method (the {\it master stability
function}), extensively used for studying the stability of the synchronous
state of networks of identical chaotic oscillators, to the case of oscillators
that are similar but not exactly identical. We find that bubbling induced
desynchronization bursts occur for some parameter values. These bursts have
spatial patterns, which can be predicted from the network connectivity matrix
and the unstable periodic orbits embedded in the attractor. We test the
analysis of bursts by comparison with numerical experiments. In the case that
no bursting occurs, we discuss the deviations from the exactly synchronous
state caused by the mismatch between oscillators
Coupled Oscillators with Chemotaxis
A simple coupled oscillator system with chemotaxis is introduced to study
morphogenesis of cellular slime molds. The model successfuly explains the
migration of pseudoplasmodium which has been experimentally predicted to be
lead by cells with higher intrinsic frequencies. Results obtained predict that
its velocity attains its maximum value in the interface region between total
locking and partial locking and also suggest possible roles played by partial
synchrony during multicellular development.Comment: 4 pages, 5 figures, latex using jpsj.sty and epsf.sty, to appear in
J. Phys. Soc. Jpn. 67 (1998
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