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Chaos / Volume 21 / Issue 4 / REGULAR ARTICLES

Chaos 21, 043125 (2011); http://dx.doi.org/10.1063/1.3660327 (11 pages)

Chaotic phase synchronization in a modular neuronal network of small-world subnetworks

Haitao Yu1, Jiang Wang1, Qiuxiang Liu2, Jinxin Wen1, Bin Deng1, and Xile Wei1

1School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, People’s Republic of China
2School of Computer Science and Engineering, Hebei University of Technology, Tianjin 300401, People’s Republic of China

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(Received 10 September 2011; accepted 24 October 2011; published online 16 November 2011)

We investigate the onset of chaotic phase synchronization of bursting oscillators in a modular neuronal network of small-world subnetworks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that this bursting synchronization transition can be induced not only by the variations of inter- and intra-coupling strengths but also by changing the probability of random links between different subnetworks. We also analyze the effect of external chaotic phase synchronization of bursting behavior in this clustered network by an external time-periodic signal applied to a single neuron. Simulation results demonstrate a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this synchronization region increases with the signal amplitude and the number of driven neurons but decreases rapidly with the network size. Considering that the synchronization of bursting neurons is thought to play a key role in some pathological conditions, the presented results could have important implications for the role of externally applied driving signal in controlling bursting activity in neuronal ensembles.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. NEURON DYNAMICS AND PHASE SYNCHRONIZATION
  3. CHAOTIC PHASE SYNCHRONIZATION IN A MODULAR NEURONAL NETWORK
    1. Modular neuronal network
    2. Chaotic phase synchronization of bursting neurons
  4. EXTERNAL CHAOTIC PHASE SYNCHRONIZATION
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

chaos, complex networks, neural nets, probability, random processes, synchronisation

PACS

  • 05.45.Xt

    Synchronization; coupled oscillators

  • 02.50.Cw

    Probability theory

  • 05.90.+m

    Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)

  • 05.40.-a

    Fluctuation phenomena, random processes, noise, and Brownian motion

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3660327

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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