Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability

¹  State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University - Beijing 100871, China
²  School of Statistics and Mathematics, Inner Mongolia Finance and Economics College - Huhhot 010051, China
³  Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor Koroška cesta 160, SI-2000 Maribor, Slovenia, EU
⁴  Department of Electronic Engineering, City University of Hong Kong - Hong Kong SAR, China

Corresponding author: nmqingyun@163.com

Received: 24 May 2008
Accepted: 15 July 2008

Abstract

Synchronization transitions are investigated in small-world neuronal networks that are locally modeled by the Rulkov map with additive spatiotemporal noise. In particular, we investigate the impact of different information transmission delays and rewiring probability. We show that short delays induce zigzag fronts of excitations, whereas intermediate delays can further detriment synchrony in the network due to a dynamic clustering anti-phase synchronization transition. Detailed investigations reveal, however, that for longer delay lengths the synchrony of excitations in the network can again be enhanced due to the emergence of in-phase synchronization. In addition, we show that an appropriate small-world topology can restore synchronized behavior provided information transmission delays are either short or long. On the other hand, within the intermediate delay region, which is characterized by anti-phase synchronization and clustering, differences in the network topology do not notably affect the synchrony of neuronal activity.