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Delayed feedback control of phase synchronisation in a neuronal network model

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Abstract

The human cerebral cortex can be separated into cortical areas forming a clustered network structure. We build two different clustered networks, where one network is based on a healthy brain and the other according to a brain affected by a neurodegenerative process. Each cortical area has a subnetwork with small-world properties. We verify that both networks exhibit rich-club organisation and phase synchronisation. Due to the fact that neuronal synchronisation can be related to brain diseases, we consider the delayed feedback control as a method to suppress synchronous behaviours. In this work, it is presented that depending on the feedback parameters, intensity and time delay, phase synchronisation in both networks can be suppressed. Therefore, one of our main results is to show that delayed feedback control can be used to suppress undesired synchronous behaviours not only in the healthy brain, but also in the brain marked by neurodegenerative processes.

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Authors and Affiliations

  1. Graduate in Science Program, State University of Ponta Grossa, Ponta Grossa, PR, Brazil

    Michele Mugnaine, Jose D. Szezech Jr. & Antonio M. Batista

  2. Physics Department, Federal University of Paraná, Curitiba, PR, Brazil

    Adriane S. Reis & Ricardo L. Viana

  3. Center for Mathematics, Computation, and Cognition, Federal University of ABC, São Bernardo do Campo, SP, Brazil

    Fernando S. Borges

  4. Department of Mathematics, Federal Technological University of Paraná, Ponta Grossa, PR, Brazil

    Rafael R. Borges

  5. Federal University of Vales of Jequitinhonha and Macuri, Institute of Engineering, Science and Technology, Janaúba, MG, Brazil

    Fabiano A. S. Ferrari

  6. Physics Institute, University of São Paulo, São Paulo, SP, Brazil

    Kelly C. Iarosz & Ibere L. Caldas

  7. Department of Physics, Humboldt University, Berlin, Germany

    Kelly C. Iarosz, Ewandson L. Lameu & Jürgen Kurths

  8. Potsdam Institute for Climate Impact Research, Potsdam, Germany

    Kelly C. Iarosz, Jürgen Kurths & Antonio M. Batista

  9. National Institute for Space Research, São José dos Campos, SP, Brazil

    Ewandson L. Lameu

  10. Department of Mathematics and Statistics, State University of Ponta Grossa, PR, Brazil

    Jose D. Szezech Jr. & Antonio M. Batista

Authors
  1. Michele Mugnaine
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  2. Adriane S. Reis
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  3. Fernando S. Borges
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  4. Rafael R. Borges
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  5. Fabiano A. S. Ferrari
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  6. Kelly C. Iarosz
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  7. Ibere L. Caldas
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  8. Ewandson L. Lameu
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  9. Ricardo L. Viana
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  10. Jose D. Szezech Jr.
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  11. Jürgen Kurths
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  12. Antonio M. Batista
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Corresponding author

Correspondence to Ricardo L. Viana.

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Mugnaine, M., Reis, A.S., Borges, F.S. et al. Delayed feedback control of phase synchronisation in a neuronal network model. Eur. Phys. J. Spec. Top. 227, 1151–1160 (2018). https://doi.org/10.1140/epjst/e2018-800031-y

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  • DOI: https://doi.org/10.1140/epjst/e2018-800031-y

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