1,357 research outputs found
Observability and Synchronization of Neuron Models
Observability is the property that enables to distinguish two different
locations in -dimensional state space from a reduced number of measured
variables, usually just one. In high-dimensional systems it is therefore
important to make sure that the variable recorded to perform the analysis
conveys good observability of the system dynamics. In the case of networks
composed of neuron models, the observability of the network depends
nontrivially on the observability of the node dynamics and on the topology of
the network. The aim of this paper is twofold. First, a study of observability
is conducted using four well-known neuron models by computing three different
observability coefficients. This not only clarifies observability properties of
the models but also shows the limitations of applicability of each type of
coefficients in the context of such models. Second, a multivariate singular
spectrum analysis (M-SSA) is performed to detect phase synchronization in
networks composed by neuron models. This tool, to the best of the authors'
knowledge has not been used in the context of networks of neuron models. It is
shown that it is possible to detect phase synchronization i)~without having to
measure all the state variables, but only one from each node, and ii)~without
having to estimate the phase
Synchronization Transition of Identical Phase Oscillators in a Directed Small-World Network
We numerically study a directed small-world network consisting of
attractively coupled, identical phase oscillators. While complete
synchronization is always stable, it is not always reachable from random
initial conditions. Depending on the shortcut density and on the asymmetry of
the phase coupling function, there exists a regime of persistent chaotic
dynamics. By increasing the density of shortcuts or decreasing the asymmetry of
the phase coupling function, we observe a discontinuous transition in the
ability of the system to synchronize. Using a control technique, we identify
the bifurcation scenario of the order parameter. We also discuss the relation
between dynamics and topology and remark on the similarity of the
synchronization transition to directed percolation.Comment: This article has been accepted in AIP, Chaos. After it is published,
it will be found at http://chaos.aip.org/, 12 pages, 9 figures, 1 tabl
Controlling spatiotemporal chaos in oscillatory reaction-diffusion systems by time-delay autosynchronization
Diffusion-induced turbulence in spatially extended oscillatory media near a
supercritical Hopf bifurcation can be controlled by applying global time-delay
autosynchronization. We consider the complex Ginzburg-Landau equation in the
Benjamin-Feir unstable regime and analytically investigate the stability of
uniform oscillations depending on the feedback parameters. We show that a
noninvasive stabilization of uniform oscillations is not possible in this type
of systems. The synchronization diagram in the plane spanned by the feedback
parameters is derived. Numerical simulations confirm the analytical results and
give additional information on the spatiotemporal dynamics of the system close
to complete synchronization.Comment: 19 pages, 10 figures submitted to Physica
General mechanism for amplitude death in coupled systems
We introduce a general mechanism for amplitude death in coupled
synchronizable dynamical systems. It is known that when two systems are coupled
directly, they can synchronize under suitable conditions. When an indirect
feedback coupling through an environment or an external system is introduced in
them, it is found to induce a tendency for anti-synchronization. We show that,
for sufficient strengths, these two competing effects can lead to amplitude
death. We provide a general stability analysis that gives the threshold values
for onset of amplitude death. We study in detail the nature of the transition
to death in several specific cases and find that the transitions can be of two
types - continuous and discontinuous. By choosing a variety of dynamics for
example, periodic, chaotic, hyper chaotic, and time-delay systems, we
illustrate that this mechanism is quite general and works for different types
of direct coupling, such as diffusive, replacement, and synaptic couplings and
for different damped dynamics of the environment.Comment: 12 pages, 17 figure
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