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Chimera States in Complex Networks

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Front. Appl. Math. Stat. | doi: 10.3389/fams.2018.00067

Control of chimera states in multilayer networks

  • 1Technische Universität Berlin, Germany

Chimera states are intriguing complex spatio-temporal patterns of coexisting coherent and
incoherent domains. They can often be observed in networks with nonlocal coupling topology,
where each element interacts with its neighbours within a fixed range. In small-size nonlocally
coupled networks, chimera states usually exhibit short lifetimes and erratic drifting of the spatial
position of the incoherent domain. This problem can be solved with a tweezer feedback control
which can stabilize and fix the position of chimera states. We analyse the action of the tweezer
control in two-layer networks, where each layer is a small nonlocally coupled ring of Van der Pol
oscillators. We demonstrate that tweezer control, applied to only one layer, successfully stabilizes
chimera patterns in the other, uncontrolled layer, even in the case of nonidentical layers. These
results might be useful for applications in multilayer networks, where one of the layers cannot be
directly accessed, thus it can be effectively controlled via a neighbouring layer.

Keywords: Dynamical systems,', chimera states, Multilayer networks, feedback control, Van der Pol oscillators

Received: 30 Oct 2018; Accepted: 27 Dec 2018.

Edited by:

Jun Ma, Lanzhou University of Technology, China

Reviewed by:

Vesna I. Berec, University of Belgrade, Serbia
Dibakar Ghosh, Indian Statistical Institute, India  

Copyright: © 2018 Omelchenko, Hülser, Zakharova and Schöll. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Iryna Omelchenko, Technische Universität Berlin, Berlin, Germany, iryna.omelchenko@tu-berlin.de