Regular Article

Effects of partial time delays on synchronization patterns in Izhikevich neuronal networks

¹ Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
² School of Engineering, RMIT University, Melbourne, Australia
³ Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
⁴ Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria

^a e-mail: matjaz.perc@gmail.com

Received: 31 October 2018
Received in final form: 10 December 2018
Published online: 13 February 2019

Abstract

Synchronization patterns have been observed in neuronal networks and are related to many cognitive functions and information processing and even some pathological brain states. In this paper, we study a ring network of non-locally coupled Izhikevich neurons with electrical synaptic coupling. Since it has been proved that time delays through gap junctions can simplify the synchronization, here we particularly investigate the effects of partial time delays on networks synchronization. By using two control parameters, the time delay and the probability of partial time delay, we show that partial time delays have a significant effect on the synchronization of this network. In particular, partial time delays can either increase or decrease the synchronization and also can induce synchronization transitions between coherent and incoherent states. Thus, partial time delays can cause chimera state, which is a special pattern when both synchronous and asynchronous states coexist and are strongly related to many real phenomena. Furthermore, partial time delays can change the period of synchronized neurons from period-1 to period-2 firing states that have different effects on information transmission in the brain.