AUTHOR=Omelchenko Iryna , Hülser Tobias , Zakharova Anna , Schöll Eckehard 

TITLE=Control of Chimera States in Multilayer Networks

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 4 - 2018

YEAR=2019

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2018.00067

DOI=10.3389/fams.2018.00067

ISSN=2297-4687

ABSTRACT=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.