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

Nonlinear Oscillations and Bifurcations in Silicon Photonic Microresonators

Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. We present a new analysis of the dynamics of these resonators, elucidating the mathematical origin of spontaneous oscillations and deriving predictions for observed phenomena such as a frequency comb spectrum with MHz-scale repetition rate. We test predictions through laboratory experiment and numerical simulation.Comment: Main text: 5 pages, 6 figures. Supplemental material: 12 pages, 8 figure

The tipping point: a mathematical model for the profit-driven abandonment of restaurant tipping

The custom of voluntarily tipping for services rendered has gone in and out of fashion in America since its introduction in the 19th century. Restaurant owners that ban tipping in their establishments often claim that social justice drives their decisions, but we show that rational profit-maximization may also justify the decisions. Here, we propose a conceptual model of restaurant competition for staff and customers, and we show that there exists a critical conventional tip rate at which restaurant owners should eliminate tipping to maximize profit. Because the conventional tip rate has been increasing steadily for the last several decades, our model suggests that restaurant owners may abandon tipping en masse when that critical tip rate is reached.Comment: 14 pages, 5 figures, supplementary material include

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