Daniel M. Abrams

Solvable Model for Chimera States of Coupled Oscillators

Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.

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.

Crowd synchrony on the Millennium Bridge

Soon after the crowd streamed on to Londons Millennium Bridge on the day it opened, the bridge started to sway from side to side: many pedestrians fell spontaneously into step with the bridges vibrations, inadvertently amplifying them. Here we model this unexpected and now notorious phenomenon — which was not due to the bridges innovative design as was first thought — by adapting ideas originally developed to describe the collective synchronization of biological oscillators such as neurons and fireflies. Our approach should help engineers to estimate the damping needed to stabilize other exceptionally crowded footbridges against synchronous lateral excitation by pedestrians.

CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS

Arrays of identical limit-cycle oscillators have been used to model a wide variety of pattern-forming systems, such as neural networks, convecting fluids, laser arrays and coupled biochemical oscil...

Sensory-based learning disability: Insights from brainstem processing of speech sounds

Speech-evoked auditory brainstem responses (speech-ABR) provide a reliable marker of learning disability in a substantial subgroup of individuals with language-based learning problems (LDs). Here we review work describing the properties of the speech-ABR in typically developing children and in children with LD. We also review studies on the relationships between speech-ABR and the commonly used click-ABR, and between speech-ABR and auditory processing at the level of the cortex. In a critical examination of previously published data, we conclude that as many as 40% of LDs have abnormal speech-ABRs and that these individuals are also likely to exhibit abnormal cortical processing. Yet, the profile of learning problems these individuals exhibit is unspecific. Leaving open the question of causality, these data suggest that speech-ABR can be used to identify a large sub-population of LDs, those with abnormal auditory physiological function. Further studies are required to determine the functional relationships among abnormal speech-ABR, speech perception, and the pattern of literacy-related and cognitive deficits in LD.

Dynamics of social group competition: modeling the decline of religious affiliation.

When groups compete for members, the resulting dynamics of human social activity may be understandable with simple mathematical models. Here, we apply techniques from dynamical systems and perturbation theory to analyze a theoretical framework for the growth and decline of competing social groups. We present a new treatment of the competition for adherents between religious and irreligious segments of modern secular societies and compile a new international data set tracking the growth of religious non-affiliation. Data suggest a particular case of our general growth law, leading to clear predictions about possible future trends in society.

Geometry of valley growth

Although amphitheatre-shaped valley heads can be cut by groundwater flows emerging from springs, recent geological evidence suggests that other processes may also produce similar features, thus confounding the interpretations of such valley heads on Earth and Mars. To better understand the origin of this topographic form, we combine field observations, laboratory experiments, analysis of a high-resolution topographic map and mathematical theory to quantitatively characterize a class of physical phenomena that produce amphitheatre-shaped heads. The resulting geometric growth equation accurately predicts the shape of decimetre-wide channels in laboratory experiments, 100 m-wide valleys in Florida and Idaho, and kilometre-wide valleys on Mars. We find that, whenever the processes shaping a landscape favour the growth of sharply protruding features, channels develop amphitheatre-shaped heads with an aspect ratio of n.

A model balancing cooperation and competition can explain 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 present a novel mathematical model and use it to test the idea that population-level hand preference represents a balance between selective costs and benefits arising from cooperation and competition in human evolutionary history. We use the selection of elite athletes as a test-bed for our evolutionary model and find evidence for the validity of this idea. Our model gives the first quantitative explanation for the distribution of handedness both across and within many professional sports. It also predicts strong lateralization of hand use in social species with limited combative interaction, and elucidates the absence of consistent population-level ‘pawedness’ in some animal species.

Introduction to focus issue: Patterns of network synchronization.

The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network synchronization. This includes chimera states, phenomena determined by symmetry, remote synchronization, and asymmetry-induced synchronization. This Focus Issue presents a selection of contributions at the forefront of these developments, to which this introduction is intended to offer an up-to-date foundation.

Parallels between wind and crowd loading of bridges.

Parallels between the dynamic response of flexible bridges under the action of wind and under the forces induced by crowds allow each field to inform the other. Wind-induced behaviour has been traditionally classified into categories such as flutter, galloping, vortex-induced vibration and buffeting. However, computational advances such as the vortex particle method have led to a more general picture where effects may occur simultaneously and interact, such that the simple semantic demarcations break down. Similarly, the modelling of individual pedestrians has progressed the understanding of human–structure interaction, particularly for large-amplitude lateral oscillations under crowd loading. In this paper, guided by the interaction of flutter and vortex-induced vibration in wind engineering, a framework is presented, which allows various human–structure interaction effects to coexist and interact, thereby providing a possible synthesis of previously disparate experimental and theoretical results.