Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte

Star clusters near and far; tracing star formation across cosmic time

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00690-x.Star clusters are fundamental units of stellar feedback and unique tracers of their host galactic properties. In this review, we will first focus on their constituents, i.e.\ detailed insight into their stellar populations and their surrounding ionised, warm, neutral, and molecular gas. We, then, move beyond the Local Group to review star cluster populations at various evolutionary stages, and in diverse galactic environmental conditions accessible in the local Universe. At high redshift, where conditions for cluster formation and evolution are more extreme, we are only able to observe the integrated light of a handful of objects that we believe will become globular clusters. We therefore discuss how numerical and analytical methods, informed by the observed properties of cluster populations in the local Universe, are used to develop sophisticated simulations potentially capable of disentangling the genetic map of galaxy formation and assembly that is carried by globular cluster populations.Peer reviewedFinal Accepted Versio

Oscillatory Neural Network for Image Segmentation with Biased Competition for Attention

Abstract We study the emergent properties of an artificial neural network which combines segmentation by oscillations and biased competition for perceptual processing. The aim is to progress in image segmentation by mimicking abstractly the way how the cerebral cortex works. In our model, the neurons associated with features belonging to an object start to oscillate synchronously, while competing objects oscillate with an opposing phase. The emergent properties of the network are confirmed by experiments with artificial image data.