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

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

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

Is primary angioplasty cost effective in the UK? Results of a comprehensive decision analysis

Objective: To assess the cost effectiveness of primary angioplasty, compared with medical management with thrombolytic drugs, to achieve reperfusion after acute myocardial infarction ( AMI) from the perspective of the UK NHS. Design: Bayesian evidence synthesis and decision analytic model. Methods: A systematic review was conducted and Bayesian statistical methods used to synthesise evidence from 22 randomised control trials. Resource utilisation was based on UK registry data, published literature and national databases, with unit costs taken from routine NHS sources and published literature. Main outcome measure: Costs from a health service perspective and outcomes measured as quality-adjusted life years (QALYs). Results: For the base case, the incremental cost-effectiveness ratio of primary angioplasty was pound 9241 for each additional QALY, with a probability of being cost effective of 0.90 for a cost-effectiveness threshold of pound 20 000. Results were sensitive to variations in the additional time required to initiate treatment with primary angioplasty. Conclusions: Primary angioplasty is cost effective for the treatment of AMI on the basis of threshold cost-effectiveness values used in the NHS and subject to a delay of up to about 80 minutes. These findings are mainly explained by the superior mortality benefit and the prevention of non-fatal outcomes associated with primary angioplasty for delays of up to this length

Assessing the effectiveness of primary angioplasty compared with thrombolysis and its relationship to time delay: a Bayesian evidence synthesis

Background: Meta-analyses of trials have shown greater benefits from angioplasty than thrombolysis after an acute myocardial infarction, but the time delay in initiating angioplasty needs to be considered. Objective: To extend earlier meta-analyses by considering 1- and 6-month outcome data for both forms of reperfusion. To use Bayesian statistical methods to quantify the uncertainty associated with the estimated relationships. Methods: A systematic review and meta-analysis published in 2003 was updated. Data on key clinical outcomes and the difference between time-to-balloon and time-to-needle were independently extracted by two researchers. Bayesian statistical methods were used to synthesise evidence despite differences between reported follow-up times and outcomes. Outcomes are presented as absolute probabilities of specific events and odds ratios (ORs; with 95% credible intervals (Crl)) as a function of the additional time delay associated with angioplasty. \ Results: 22 studies were included in the meta-analysis, with 3760 and 3758 patients randomised to primary angioplasty and thrombolysis, respectively. The mean ( SE) angioplasty-related time delay ( over and above time to thrombolysis) was 54.3 (2.2) minutes. For this delay, mean event probabilities were lower for primary angioplasty for all outcomes. Mortality within 1 month was 4.5% after angioplasty and 6.4% after thrombolysis ( OR = 0.68 ( 95% Crl 0.46 to 1.01)). For non-fatal reinfarction, OR = 0.32 ( 95% Crl 0.20 to 0.51); for non-fatal stroke OR = 0.24 ( 95% Crl 0.11 to 0.50). For all outcomes, the benefit of angioplasty decreased with longer delay from initiation. Conclusions: The benefit of primary angioplasty, over thrombolysis, depends on the former's additional time delay. For delays of 30-90 minutes, angioplasty is superior for 1- month fatal and non-fatal outcomes. For delays of around 90 minutes thrombolysis may be the preferred option as assessed by 6-month mortality; there is considerable uncertainty for longer time delays