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The European Physical Journal Special Topics

, Volume 227, Issue 10–11, pp 1151–1160 | Cite as

Delayed feedback control of phase synchronisation in a neuronal network model

  • Michele Mugnaine
  • Adriane S. Reis
  • Fernando S. Borges
  • Rafael R. Borges
  • Fabiano A. S. Ferrari
  • Kelly C. Iarosz
  • Ibere L. Caldas
  • Ewandson L. Lameu
  • Ricardo L. VianaEmail author
  • Jose D. SzezechJr.
  • Jürgen Kurths
  • Antonio M. Batista
Regular Article
Part of the following topical collections:
  1. Advances in Nonlinear Dynamics of Complex Networks: Adaptivity, Stochasticity, Delays

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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Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Michele Mugnaine
    • 1
  • Adriane S. Reis
    • 2
  • Fernando S. Borges
    • 3
  • Rafael R. Borges
    • 4
  • Fabiano A. S. Ferrari
    • 5
  • Kelly C. Iarosz
    • 6
    • 7
    • 8
  • Ibere L. Caldas
    • 6
  • Ewandson L. Lameu
    • 7
    • 9
  • Ricardo L. Viana
    • 2
    Email author
  • Jose D. SzezechJr.
    • 1
    • 10
  • Jürgen Kurths
    • 7
    • 8
  • Antonio M. Batista
    • 1
    • 8
    • 10
  1. 1.Graduate in Science Program, State University of Ponta GrossaPonta GrossaBrazil
  2. 2.Physics Department, Federal University of ParanáCuritibaBrazil
  3. 3.Center for Mathematics, Computation, and Cognition, Federal University of ABCSPBrazil
  4. 4.Department of MathematicsFederal Technological University of ParanáPonta GrossaBrazil
  5. 5.Federal University of Vales of Jequitinhonha and Macuri, Institute of Engineering, Science and TechnologyJanaúbaBrazil
  6. 6.Physics Institute, University of São PauloSão PauloBrazil
  7. 7.Department of PhysicsHumboldt UniversityBerlinGermany
  8. 8.Potsdam Institute for Climate Impact ResearchPotsdamGermany
  9. 9.National Institute for Space ResearchSão José dos CamposBrazil
  10. 10.Department of Mathematics and StatisticsState University of Ponta GrossaPRBrazil

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