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Synchronization in ensembles of delay-coupled nonidentical neuronlike oscillators

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Abstract

We study both numerically and experimentally the synchronization in an ensemble of nonidentical neuronlike oscillators described by the FitzHugh–Nagumo equations. The cases of constant values of time-delayed couplings between the oscillators and adaptively controlled values of time-delayed couplings are considered. For the experimental study of the ensemble of neuronlike oscillators, we construct a radio engineering setup, in which the ability to specify both constant values and adaptively tuned values of couplings between the oscillators is implemented. Moreover, it is possible to specify an arbitrary architecture and type of dynamical couplings between oscillators in the setup. By the example of a system of two bidirectionally coupled nonidentical oscillators and a ring consisting of ten unidirectionally coupled nonidentical FitzHugh–Nagumo systems, it is shown that the using of an adaptively controlled time-delayed coupling allows one to achieve the in-phase synchronization of all oscillators in the ensemble even in the case of a large parameter mismatch. The results obtained in the physical experiment are in good agreement with the results of the numerical simulation.

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Acknowledgements

This study was funded by the Russian Science Foundation (Grant No. 17-72-30003).

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Authors and Affiliations

  1. Saratov Branch of Kotel’nikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov, Russia, 410019

    D. D. Kulminskiy, V. I. Ponomarenko & M. D. Prokhorov

  2. Innopolis University, Universitetskaya Street, 1, Innopolis, Russia, 420500

    D. D. Kulminskiy, V. I. Ponomarenko, M. D. Prokhorov & A. E. Hramov

  3. Saratov State University, Astrakhanskaya Street, 83, Saratov, Russia, 410012

    D. D. Kulminskiy & V. I. Ponomarenko

  4. Saratov State Medical University, Bolshaya Kazachya Street, 112, Saratov, Russia, 410012

    A. E. Hramov

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  1. D. D. Kulminskiy
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  2. V. I. Ponomarenko
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  3. M. D. Prokhorov
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Kulminskiy, D.D., Ponomarenko, V.I., Prokhorov, M.D. et al. Synchronization in ensembles of delay-coupled nonidentical neuronlike oscillators. Nonlinear Dyn 98, 735–748 (2019). https://doi.org/10.1007/s11071-019-05224-x

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