Eur. Phys. J. B (2013) 86: 301
https://doi.org/10.1140/epjb/e2013-40078-3

Regular Article

Stimulus-induced transition of clustering firings in neuronal networks with information transmission delay

¹ Department of Dynamics and Control, Beihang University, Beijing 100191, P.R. China
² State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
³ Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P.R. China

^a e-mail: nmqingyun@163.com

Received: 30 January 2013
Received in final form: 8 April 2013
Published online: 1 July 2013

Abstract

We study the evolution of spatiotemporal dynamics and transition of clustering firing synchronization on spiking Hodgkin-Huxley neuronal networks as information transmission delay and the periodic stimulus are varied. In particular, it is shown that the tuned information transmission delay can induce a clustering anti-phase synchronization transition with the pacemaker, where two equal clusters can alternatively synchronize in anti-phase firing. More interestingly, we show that the periodic stimulus can drive the delay-induced clustering anti-phase firing synchronization bifurcate to the collective perfect synchronization, which is routed by the complex process including collective chaotic firings and clustering out-of-phase synchronization of the neuronal networks. In addition, the periodic stimulus induced clustering firings of the spiking neuronal networks are robust to the connectivity probability of small world networks. Furthermore, the different stimulus frequency induced complexity is also investigated. We hope that the results of this paper can provide insights that could facilitate the understanding of the joint impact of information transmission delays and periodic stimulus on controlling dynamical behaviors of realistic neuronal networks.