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