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

Prospettive relazionali di vulnerabilità. Lo svuotamento dei diritti umani in contesti sociali vulnerabili

In seguito al vulnerability turn che si è sviluppato nella filosofia politi- ca, il concetto di vulnerabilità è stato più volte utilizzato come supporto al principio di uguaglianza nel suo senso sostanziale. La dimensione univer- sale della vulnerabilità si riferisce a tutti gli individui come dato ontologi- co. Come già evidenziato da Butler, però, non tutti sono vulnerabili allo stesso modo, ciò suggerisce che il concetto in questione sia anche partico- lare. Questo elaborato si inserisce all’interno del dibattito sulla dimensione particolare del tema, provando a spostare il punto di vista dai soggetti ai contesti, evidenziando l’elemento relazionale nella condizione ontologica della vulnerabilità. L’obiettivo sarà quello di fornire nuove possibili spie- gazioni alla distribuzione differenziale di vulnerabilità.  Following the vulnerability turn that has developed in political phi- losophy, the concept of vulnerability has been repeatedly used to support the principle of substantive equality. The universal dimension of vulner- ability refers to all individuals as an ontological condition. However, as previously highlighted by Butler, not everyone is vulnerable in the same way, suggesting that the concept in question is also particular. This paper contributes to the debate on the particular dimension of the theme by at- tempting to shift the focus from individuals to contexts, highlighting the relational element in the ontological condition of vulnerability. The objec- tive is to provide new possible explanations for the differential distribution of vulnerability.  Parole chiave: Vulnerabilità; Relazionalità; Contesti; Disuguaglianze, Diritti Umani. Keywords: Vulnerability; Relationality; Contexts; Inequalities; Human Rights

Chaos in Kuramoto Oscillator Networks

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this record.Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme can exhibit chaotic dynamics as conjectured by Ott and Antonsen [Chaos, 18, 037113 (2008)]. These chaotic mean field dynamics arise universally across network size, from the continuum limit of infinitely many oscillators down to very small networks with just two oscillators per population. Hence, complicated dynamics are expected even in the simplest description of oscillator networks.The authors would like to thank J Engelbrecht, R Mirollo, A Politi, and M Wolfrum for helpful discussions and F Peter for careful reading of the manuscript. CB would like to acknowledge the warm hospitality at DTU. Research conducted by EAM is partially supported by the Dynamical Systems Interdisciplinary Network, University of Copenhagen. CB has received partial funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007–2013) under REA grant agreement no. 626111

Model reconstruction from temporal data for coupled oscillator networks

In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic influence over those dynamics. In many studies, researchers start with a specific model for both the intrinsic dynamics of each agent and the interaction network, and attempt to learn about the dynamics that can be observed in the model. Here we consider the inverse problem: given the dynamics of a system, can one learn about the underlying network? We investigate arbitrary networks of coupled phase-oscillators whose dynamics are characterized by synchronization. We demonstrate that, given sufficient observational data on the transient evolution of each oscillator, one can use machine learning methods to reconstruct the interaction network and simultaneously identify the parameters of a model for the intrinsic dynamics of the oscillators and their coupling.Comment: 27 pages, 7 figures, 16 table