Eur. Phys. J. Special Topics 228, 2441-2454 (2019)
https://doi.org/10.1140/epjst/e2019-900007-8

Regular Article

Intralayer synchronization in neuronal multiplex network

¹ Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India
² Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India

^a e-mail: diba.ghosh@gmail.com

Received: 22 January 2019
Received in final form: 6 March 2019
Published online: 28 October 2019

Abstract

Synchronization phenomenon is one of the most fundamental properties in the field of neurosciences, and it plays a key role in several neuronal processes. In this paper, we report a neural synchrony in a multiplex neuronal network by simultaneously taking electrical and chemical synaptic interactions. Most of the previous studies on the neuronal synchrony have been focused on a mono-layer network by solely considering one type of neuronal communication, either electrical or chemical synaptic coupling. Here we consider the multiplex network where the connection within the layer (intralayer connection) and the layer–layer interaction (interlayer connection) links are associated with the electrical and chemical synapses respectively. The network topology in each layer is represented by the small-world network. We mainly explore intralayer synchronization in the multiplex network under the simultaneous effect of both synaptic interactions. Intralayer synchronization is a distinctive process that refered to coherence among the nodes within the layer irrespective of the coherence between the replica nodes. Through the master stability approach, we derive the necessary condition for the intralayer synchronization state and then we numerically confirm our analytical findings.