Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 14: Focus Session: Chimera states: symmetry-breaking in dynamical networks (joint session DY/ BP)

DY 14.1: Hauptvortrag

Dienstag, 17. März 2015, 09:30–10:00, BH-N 243

Basins of Attraction for Chimera States — •Erik Andreas Martens^1,2, Mark Panaggio^3,4, and Daniel Abrams^4,5 — ¹Dept. of Biomedical Sciences, University of Copenhagen, Blegdamsvej 3, 2200 Copenhagen, Denmark — ²Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2200 Copenhagen, Denmark — ³Dept. of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803 — ⁴Dept. of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208 — ⁵Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA

The coexistence of synchronized and desynchronized regions in populations of identical oscillators, known as chimera states, has received much attention following their recent experimental discovery. Chimeras occur only for special initial conditions; yet, despite numerous theoretical efforts their basins of attraction remain unexplored. We provide the first analysis of their basins of attraction by studying the simplest chimera system with two populations, allowing for three configuration patterns: one fully synchronized and two partly synchronized patterns. The basins form a complex twisting motion around an invariant ray; our perturbative analysis allows the prediction of the asymptotic states and the associated destination maps. Understanding the precise nature of the basins is needed to develop control methods to switch between chimeric configuration patterns, which may may be exploited for technological applications and serve function in neural biology.