154 research outputs found
Generating macroscopic chaos in a network of globally coupled phase oscillators
We consider an infinite network of globally-coupled phase oscillators in
which the natural frequencies of the oscillators are drawn from a symmetric
bimodal distribution. We demonstrate that macroscopic chaos can occur in this
system when the coupling strength varies periodically in time. We identify
period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for
the macroscopic mean field. Based on recent work that clarified the bifurcation
structure of the static bimodal Kuramoto system, we qualitatively describe the
mechanism for the generation of such complicated behavior in the time varying
case
The Onset of Synchronization in Systems of Globally Coupled Chaotic and Periodic Oscillators
A general stability analysis is presented for the determination of the
transition from incoherent to coherent behavior in an ensemble of globally
coupled, heterogeneous, continuous-time dynamical systems. The formalism allows
for the simultaneous presence of ensemble members exhibiting chaotic and
periodic behavior, and, in a special case, yields the Kuramoto model for
globally coupled periodic oscillators described by a phase. Numerical
experiments using different types of ensembles of Lorenz equations with a
distribution of parameters are presented.Comment: 26 pages and 26 figure
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
The Breakdown of Synchronization in Systems of Non-identical Chaotic Oscillators: Theory and Experiment
The synchronization of chaotic systems has received a great deal of attention. However, most of the literature has focused on systems that possess invariant manifolds that persist as the coupling is varied. In this paper, we describe the process whereby synchronization is lost in systems of nonidentical coupled chaotic oscillators without special symmetries. We qualitatively and quantitatively analyze such systems in terms of the evolution of the unstable periodic orbit structure. Our results are illustrated with data from physical experiments
Networks of theta neurons with time-varying excitability: macroscopic chaos, multistability, and final-state uncertainty, Physica D 267
h i g h l i g h t s • Derived exact asymptotic dynamics for time-varying networks of theta neurons. • Network exhibited macroscopic chaos, quasiperiodicity, and multistability. • Network exhibited fractal basin boundaries and final-state uncertainty. • Escape and switching behaviors depend on both macroscopic and microscopic initial states. • Ability to redirect such macroscopic states with an accessible global parameter. a r t i c l e i n f o b s t r a c t Using recently developed analytical techniques, we study the macroscopic dynamics of a large heterogeneous network of theta neurons in which the neurons' excitability parameter varies in time. We demonstrate that such periodic variation can lead to the emergence of macroscopic chaos, multistability, and final-state uncertainty in the collective behavior of the network. Finite-size network effects and rudimentary control via an accessible macroscopic network parameter is also investigated
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