WIAS Preprint No. 2449, (2017)

Optimal design of the tweezer control for chimera states



Authors

  • Omelchenko, Iryna
  • Omel'chenko, Oleh E.
    ORCID: 0000-0003-0526-1878
  • Zakharova, Anna
  • Schöll, Eckehard

2010 Mathematics Subject Classification

  • 34H10 34C15

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt 05.45.Ra 89.75.-k

Keywords

  • Nonlinear systems, dynamical networks, spatial chaos, chimera state, feedback control

DOI

10.20347/WIAS.PREPRINT.2449

Abstract

Chimera states are complex spatio-temporal patterns, which consist of coexisting domains of spatially coherent and incoherent dynamics in systems of coupled oscillators. In small networks, chimera states usually exhibit short lifetimes and erratic drifting of the spatial position of the incoherent domain. A tweezer feedback control scheme can stabilize and fix the position of chimera states. We analyse the action of the tweezer control in small nonlocally coupled networks of Van der Pol and FitzHugh--Nagumo oscillators, and determine the ranges of optimal control parameters. We demonstrate that the tweezer control scheme allows for stabilization of chimera states with different shapes, and can be used as an instrument for controlling the coherent domains size, as well as the maximum average frequency difference of the oscillators.

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