Eur. Phys. J. Special Topics 229, 2205–2214 (2020)
https://doi.org/10.1140/epjst/e2020-900270-4

Regular Article

Minimal chimera states in phase-lag coupled mechanical oscillators

¹ Forschungszentrum Jülich GmbH, ZEA-2: Electronics Systems, 52428 Jülich, Germany
² Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland
³ Department of Electronics and Informatics, University Duisburg-Essen, Duisburg, Germany
⁴ Institute of Mathematics and Center for Medical and Biotechnical Research, National Academy of Science of Ukraine, Tereshchenkivska St. 3, 01030 Kyiv, Ukraine

^a e-mail: p.ebrahimzadeh@fz-juelich.de

Received: 29 November 2019
Accepted: 8 June 2020
Published online: 28 September 2020

Abstract

We obtain experimental chimera states in the minimal network of three identical mechanical oscillators (metronomes), by introducing phase-lagged all-to-all coupling. For this, we have developed a real-time model-in-the-loop coupling mechanism that allows for flexible and online change of coupling topology, strength and phase-lag. The chimera states manifest themselves as a mismatch of average frequency between two synchronous and one desynchronized oscillator. We find this kind of striking “chimeric” behavior is robust in a wide parameter region. At other parameters, however, chimera state can lose stability and the system behavior manifests itself as a heteroclinic switching between three saddle-type chimeras. Our experimental observations are in a qualitative agreement with the model simulation.