Eur. Phys. J. Special Topics 227, 1151–1160 (2018)
https://doi.org/10.1140/epjst/e2018-800031-y

Regular Article

Delayed feedback control of phase synchronisation in a neuronal network model

¹ Graduate in Science Program, State University of Ponta Grossa, Ponta Grossa, PR, Brazil
² Physics Department, Federal University of Paraná, Curitiba, PR, Brazil
³ Center for Mathematics, Computation, and Cognition, Federal University of ABC, São Bernardo do Campo, SP, Brazil
⁴ Department of Mathematics, Federal Technological University of Paraná, Ponta Grossa, PR, Brazil
⁵ Federal University of Vales of Jequitinhonha and Macuri, Institute of Engineering, Science and Technology, Janaúba, MG, Brazil
⁶ Physics Institute, University of São Paulo, São Paulo, SP, Brazil
⁷ Department of Physics, Humboldt University, Berlin, Germany
⁸ Potsdam Institute for Climate Impact Research, Potsdam, Germany
⁹ National Institute for Space Research, São José dos Campos, SP, Brazil
¹⁰ Department of Mathematics and Statistics, State University of Ponta Grossa, PR, Brazil

^a e-mail: viana@fisica.ufpr.br

Received: 26 March 2018
Received in final form: 6 June 2018
Published online: 12 December 2018

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.