Eur. Phys. J. Special Topics 228, 2391-2403 (2019)
https://doi.org/10.1140/epjst/e2019-900052-3

Regular Article

Synchronization in a multilayer neuronal network: effect of time delays

¹ Shaanxi Engineering Research Center of Controllable Neutron Source, School of Science, Xijing University, Xi’an 710123, P.R. China
² Department of information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah, Saudi Arabia
³ Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

^a e-mail: phamvietthanh@tdtu.edu.vn

Received: 8 March 2019
Received in final form: 8 April 2019
Published online: 28 October 2019

Abstract

Multilayer neuronal networks provide the opportunity of considering multiple types of synaptic connections. In this paper, a two-layer neuronal network with chemical intralayer connections and electrical interlayer connections is investigated, where two layers have different spiking and bursting behaviours. The effects of synaptic time delay and also the self-feedback time delay on the synchronization are studied by calculating a statistical synchronization factor for intralayer synchronization and defining an interlayer synchronization error. It is observed that the interlayer coupling strength changes the spiking behaviour of first-layer neurons toward the chaotic behaviour of the second layer. The intralayer coupling is effective on the collective behaviour of the layers. Computing the synchronization measures for the time delays separately, shows the effects of each time delay on the network’s synchronized behaviour. It also reveals that the lowest interlayer synchronization error and the highest intralayer synchronization factors are attained by using the self-feedback delay.