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

• Published in: The European physical journal. B, Condensed matter physics Vol. 86; no. 7
• Main Authors: Wang, Qingyun, Zhang, Honghui, Chen, Guanrong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2013; EDP Sciences; Springer
• Subjects: Applied sciences; Artificial intelligence; Biological and medical sciences; Central nervous system; Complex Systems; Computer science; control theory; systems; Condensed Matter Physics; Connectionism. Neural networks; Employee dismissals; Exact sciences and technology; Fluid- and Aerodynamics; Fundamental and applied biological sciences. Psychology; Information management; Neurons; Nonlinear dynamics and nonlinear dynamical systems; Physics; Physics and Astronomy; Regular Article; Solid State Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Synchronization ; coupled oscillators; Vertebrates: nervous system and sense organs; Statistical and Nonlinear Physics; Chaos; Stimulus; Small world effect; Probabilistic approach; Hodgkin Huxley model; Phase synchronization; Cluster; Stimulus complexity; Collective process; Neural network; Phase transitions; Delay
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2013-40078-3

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.