3,543 research outputs found
Control of unstable steady states by extended time-delayed feedback
Time-delayed feedback methods can be used to control unstable periodic orbits
as well as unstable steady states. We present an application of extended time
delay autosynchronization introduced by Socolar et al. to an unstable focus.
This system represents a generic model of an unstable steady state which can be
found for instance in a Hopf bifurcation. In addition to the original
controller design, we investigate effects of control loop latency and a
bandpass filter on the domain of control. Furthermore, we consider coupling of
the control force to the system via a rotational coupling matrix parametrized
by a variable phase. We present an analysis of the domain of control and
support our results by numerical calculations.Comment: 11 pages, 16 figure
Cluster and group synchronization in delay-coupled networks
We investigate the stability of synchronized states in delay-coupled networks
where synchronization takes place in groups of different local dynamics or in
cluster states in networks with identical local dynamics. Using a master
stability approach, we find that the master stability function shows a discrete
rotational symmetry depending on the number of groups. The coupling matrices
that permit solutions on group or cluster synchronization manifolds show a very
similar symmetry in their eigenvalue spectrum, which helps to simplify the
evaluation of the master stability function. Our theory allows for the
characterization of stability of different patterns of synchronized dynamics in
networks with multiple delay times, multiple coupling functions, but also with
multiple kinds of local dynamics in the networks' nodes. We illustrate our
results by calculating stability in the example of delay-coupled semiconductor
lasers and in a model for neuronal spiking dynamics.Comment: 11 pages, 7 figure
Experimental Observations of Group Synchrony in a System of Chaotic Optoelectronic Oscillators
We experimentally demonstrate group synchrony in a network of four nonlinear
optoelectronic oscillators with time-delayed coupling. We divide the nodes into
two groups of two each, by giving each group different parameters and by
enabling only inter-group coupling. When coupled in this fashion, the two
groups display different dynamics, with no isochronal synchrony between them,
but the nodes in a single group are isochronally synchronized, even though
there is no intra-group coupling. We compare experimental behavior with
theoretical and numerical results
Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators
We consider networks of delay-coupled Stuart-Landau oscillators. In these
systems, the coupling phase has been found to be a crucial control parameter.
By proper choice of this parameter one can switch between different synchronous
oscillatory states of the network. Applying the speed-gradient method, we
derive an adaptive algorithm for an automatic adjustment of the coupling phase
such that a desired state can be selected from an otherwise multistable regime.
We propose goal functions based on both the difference of the oscillators and a
generalized order parameter and demonstrate that the speed-gradient method
allows one to find appropriate coupling phases with which different states of
synchronization, e.g., in-phase oscillation, splay or various cluster states,
can be selected.Comment: 8 pages, 7 figure
Symmetry-breaking transitions in networks of nonlinear circuit elements
We investigate a nonlinear circuit consisting of N tunnel diodes in series,
which shows close similarities to a semiconductor superlattice or to a neural
network. Each tunnel diode is modeled by a three-variable FitzHugh-Nagumo-like
system. The tunnel diodes are coupled globally through a load resistor. We find
complex bifurcation scenarios with symmetry-breaking transitions that generate
multiple fixed points off the synchronization manifold. We show that multiply
degenerate zero-eigenvalue bifurcations occur, which lead to multistable
current branches, and that these bifurcations are also degenerate with a Hopf
bifurcation. These predicted scenarios of multiple branches and degenerate
bifurcations are also found experimentally.Comment: 32 pages, 11 figures, 7 movies available as ancillary file
Direct photons ~basis for characterizing heavy ion collisions~
After years of experimental and theoretical efforts, direct photons become a
strong and reliable tool to establish the basic characteristics of a hot and
dense matter produced in heavy ion collisions. The recent direct photon
measurements are reviewed and a future prospect is given.Comment: 8 pages, 8 figures, Invited plenary talk at Quark Matter 200
Genetic diversity and origin of the feral horses in Theodore Roosevelt National Park
Feral horses in Theodore Roosevelt National Park (TRNP) represent an iconic era of the North Dakota Badlands. Their uncertain history raises management questions regarding origins, genetic diversity, and long-term genetic viability. Hair samples with follicles were collected from 196 horses in the Park and used to sequence the control region of mitochondrial DNA (mtDNA) and to profile 12 autosomal short tandem repeat (STR) markers. Three mtDNA haplotypes found in the TRNP horses belonged to haplogroups L and B. The control region variation was low with haplotype diversity of 0.5271, nucleotide diversity of 0.0077 and mean pairwise difference of 2.93. We sequenced one mitochondrial genome from each haplotype determined by the control region. Two complete mtDNA sequences of haplogroup L were closely related to the mtDNA of American Paint horse. The TRNP haplotype B did not have close matches in GenBank. The phylogenetic test placed this sequence in a group consisting of two horses from China, one from Yakutia, and one from Italy raising a possibility of historical transportation of horses from Siberia and East Asia to North America. Autosomal STR loci were polymorphic and indicated that the TRNP horses were distinctly different from 48 major horse breeds. Heterozygosity, mean number of alleles, and other measures of diversity indicated that TRNP herd diversity was below that observed for most other feral herds and domestic breeds. Both mtDNA and STRs demonstrated that the existing genetic data sets of horses are insufficient to determine the exact origins of the TRNP horses. However, measures of nuclear and mitochondrial diversity have elucidated management needs. It is recommended that new genetic stock be introduced and that adaptive management principles are employed to ensure that unique mitochondrial lineages are preserved and genetic diversity is increased and maintained over time
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