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Phase-selective entrainment of nonlinear oscillator ensembles

Author

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  • Anatoly Zlotnik

    (Center for Nonlinear Studies, MS B258, Los Alamos National Laboratory)

  • Raphael Nagao

    (Saint Louis University)

  • István Z. Kiss

    (Saint Louis University)

  • Jr-Shin Li

    (Washington University in St Louis)

Abstract

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.

Suggested Citation

  • Anatoly Zlotnik & Raphael Nagao & István Z. Kiss & Jr-Shin Li, 2016. "Phase-selective entrainment of nonlinear oscillator ensembles," Nature Communications, Nature, vol. 7(1), pages 1-7, April.
  • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms10788
    DOI: 10.1038/ncomms10788
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    Cited by:

    1. Bomela, Walter & Zlotnik, Anatoly & Li, Jr-Shin, 2018. "A phase model approach for thermostatically controlled load demand response," Applied Energy, Elsevier, vol. 228(C), pages 667-680.

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