Eur. Phys. J. Special Topics 228, 2419-2427 (2019)
https://doi.org/10.1140/epjst/e2019-900014-7

Regular Article

Synchronization and chimera states in a multilayer neuronal network with unidirectional interlayer links

¹ Institute of Chinese Materia Medica, Gansu Provincial Hospital of Traditional Chinese Medicine, Lanzhou 730050, P.R. China
² Department of Rehabilitation Medicine, Gansu Provincial Hospital of Traditional Chinese Medicine, Lanzhou 730050, P.R. China
³ Department of Rehabilitation and Physiotherapy, Gansu Provincial Hospital, Lanzhou 730000, P.R. China

^a e-mail: lijuan966@163.com

Received: 26 January 2019
Received in final form: 17 February 2019
Published online: 28 October 2019

Abstract

The brain consists of many interconnected systems and subsystems that have unidirectional or bidirectional connectivities. In this paper, we consider a two-layer neuronal network with unidirectional interlayer connections to investigate the effects of one layer on the other one. Two one-dimensional ring networks with non-local couplings construct the two-layer network. The couplings are considered to be linear to describe the electrical synapses. At first, the independent layer, which is not affected by the other layer, is analysed. Different patterns such as synchronizations, non-stationary chimera state and imperfect synchronization are observed in such solo network. Then the two-layer network is investigated by varying three coupling strengths of intra-layer and inter-layer links. The results show that the first layer can change the behaviour of neurons in the second layer according to the values of coupling strengths. The interaction of the interlayer and intralayer couplings can also induce the emergence of imperfect chimera state, which was not observed in the monolayer network. These self-organized phenomena can have strong relations with brain functions and malfunctions.