Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking

Qingyun Wang; Xia Shi; Guanrong Chen

doi:10.3934/dcdsb.2011.16.607

Article Contents

2011, Volume 16, Issue 2: 607-621. Doi: 10.3934/dcdsb.2011.16.607

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Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking

1.
Department of Dynamics and Control, Beihang University, Beijing 100191
2.
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876
3.
Department of Electronic Engineering, City University of Hong Kong, Hong Kong

Received: December 2009

Revised: September 2010

Published: September 2011

Abstract / Introduction Related Papers Cited by

Abstract

We study the evolution of spatiotemporal dynamics and synchronization transition on small-world Hodgkin-Huxley (HH) neuronal networks that are characterized with channel noises, ion channel blocking and information transmission delays. In particular, we examine the effects of delay on spatiotemporal dynamics over neuronal networks when channel blocking of potassium or sodium is involved. We show that small delays can detriment synchronization in the network due to a dynamic clustering anti-phase synchronization transition. We also show that regions of irregular and regular wave propagations related to synchronization transitions appear intermittently as the delay increases, and the delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony. In addition, we show that the fraction of sodium or potassium channels can play a key role in dynamics of neuronal networks. Furthermore, We found that the fraction of sodium and potassium channels has different impacts on spatiotemporal dynamics of neuronal networks, respectively. Our results thus provide insights that could facilitate the understanding of the joint impact of ion channel blocking and information transmission delays on the dynamical behaviors of realistic neuronal networks.

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Mathematics Subject Classification: 76R10, 76F70.

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