Synchronous firings in small-world networks of excitable nodes

¹ Department of Physics, Beijing Normal University - Beijing 100875, China
² Hangzhou Normal University - Hangzhou 310036, China
³ State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University - Beijing, China
⁴ Center for Systems Biology, Soochow University - Suzhou, Jiangsu 215006, China

^(a) ganghu@bnu.edu.cn
^(b) miyuanyuan0102@163.com

Received: 13 January 2013
Accepted: 2 April 2013

Abstract

The phenomenon of synchronous firings is investigated in excitable small-world networks (ESWNs) of 2D lattices. Two sharply different types of patterns, wavelet turbulence (WT) patterns and synchronous firing (SF) patterns, and the associated transitions and hysteresis are found in wide parameter regions and in different excitable models. The WT state is maintained by wavelet defects while the SF state is due to iterative excitations between majority nodes and minority nodes where defects do not play essential roles. Moreover, a dominant phase-advanced driving method is applied to explain how self-sustained SFs can be maintained in ESWN and why SF and WT states show distinctive characteristic features. Since excitability of node and small-world network structure are two essential ingredients of some neural subsystems and SFs are important for many neural functions, the results in this paper are thus expected to be instructive for understanding the dynamics of some neural networks.