Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators

A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually coexists with a stable spatially symmetric state, has intrigued the nonlinear dynamics community since its discovery in the early 2000s. Recent experiments have led to increasing interest in the origin and dynamics of these states. Here we review the history of research on chimera states and highlight major advances in understanding their behaviour.Comment: 26 pages, 3 figure

Detection of alteration associated with a porphyry copper deposit in southern Arizona

Computer processing of Landsat MSS data was performed using contrast stretching and band-to-band ratioing. A false color ratio composite picture showed color anomalies which coincided with known areas of alteration on and about Red Mountain. A helicopter survey of the study area was undertaken using a portable field reflectance spectrometer. One hundred fifty-six spectra were obtained in the 0.4 to 2.5 micrometer wavelength region. The spectra were digitized, and contour maps for 24 wavelength intervals were produced; no spectral anomalies were evident for the known altered areas. A contour map produced from the 1.6 and 2.2 micrometer ratio generally delineated the alteration areas. The 1.3, 1.6, and 2.2 micrometer wavelength data were canonically transformed using a transformation empirically derived from discriminant function analysis of altered and unaltered materials for the Goldfield, Nevada region, and a contour map was produced for the first canonical variable. The known areas of alteration were clearly defined on the contour map

Basins of Attraction for Chimera States

Chimera states---curious symmetry-broken states in systems of identical coupled oscillators---typically occur only for certain initial conditions. Here we analyze their basins of attraction in a simple system comprised of two populations. Using perturbative analysis and numerical simulation we evaluate asymptotic states and associated destination maps, and demonstrate that basins form a complex twisting structure in phase space. Understanding the basins' precise nature may help in the development of control methods to switch between chimera patterns, with possible technological and neural system applications.Comment: Please see Ancillary files for the 4 supplementary videos including description (PDF

A model balancing cooperation and competition explains our right-handed world and the dominance of left-handed athletes

An overwhelming majority of humans are right-handed. Numerous explanations for individual handedness have been proposed, but this population-level handedness remains puzzling. Here we use a minimal mathematical model to explain this population-level hand preference as an evolved balance between cooperative and competitive pressures in human evolutionary history. We use selection of elite athletes as a test-bed for our evolutionary model and account for the surprising distribution of handedness in many professional sports. Our model predicts strong lateralization in social species with limited combative interaction, and elucidates the rarity of compelling evidence for "pawedness" in the animal world.Comment: 5 pages of text and 3 figures in manuscript, 8 pages of text and two figures in supplementary materia

Tunable Oscillations in the Purkinje Neuron

In this paper, we study the dynamics of slow oscillations in Purkinje neurons in vitro, and derive a strong association with a forced parametric oscillator model. We demonstrate the precise rhythmicity of the oscillations in Purkinje neurons, as well as a dynamic tunability of this oscillation using a photo-switchable compound. We show that this slow oscillation can be induced in every Purkinje neuron, having periods ranging between 10-25 seconds. Starting from a Hodgkin-Huxley model, we also demonstrate that this oscillation can be externally modulated, and that the neurons will return to their intrinsic firing frequency after the forced oscillation is concluded. These results signify an additional functional role of tunable oscillations within the cerebellum, as well as a dynamic control of a time scale in the brain in the range of seconds.Comment: 12 pages, 5 figure

Evaluation of LANDSAT MSS vs TM simulated data for distinguishing hydrothermal alteration

The LANDSAT Follow-On (LFO) data was simulated to demonstrate the mineral exploration capability of this system for segregating different types of hydrothermal alteration and to compare this capability with that of the existing LANDSAT system. Multispectral data were acquired for several test sites with the Bendix 24-channel MSDS scanner. Contrast enhancements, band ratioing, and principal component transformations were used to process the simulated LFO data for analysis. For Red Mountain, Arizona, the LFO data allowed identification of silicified areas, not identifiable with LANDSAT 1 and 2 data. The improved LFO resolution allowed detection of small silicic outcrops and of a narrow silicified dike. For Cuprite - Ralston, Nevada, the LFO spectral bands allowed discrimination of argillic and opalized altered areas; these could not be spectrally discriminated using LANDSAT 1 and 2 data. Addition of data from the 1.3- and 2.2- micrometer regions allowed better discriminations of hydrothermal alteration types

A study of alteration associated with uranium occurrences in sandstone and its detection by remote sensing methods, volume 2

This document contains tabular and graphic data for volume 1

Chimera states in networks of phase oscillators: the case of two small populations

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of $2N$ phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for $N>2$ the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.Comment: 13 pages, 16 figure