中国物理B ›› 2009, Vol. 18 ›› Issue (2): 482-488.doi: 10.1088/1674-1056/18/2/018

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Complete and phase synchronization in a heterogeneous small-world neuronal network

Wiercigroch Marian1, 季全宝2, 韩芳3, 陆启韶3   

  1. (1)School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK; (2)School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China; (3)School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • 收稿日期:2008-03-29 修回日期:2008-06-23 出版日期:2009-02-20 发布日期:2009-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10872014).

Complete and phase synchronization in a heterogeneous small-world neuronal network

Han Fang(韩芳)a), Lu Qi-Shao(陆启韶)a)†, Wiercigroch Marianb), and Ji Quan-Bao(季全宝)a)   

  1. a School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China; b School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK
  • Received:2008-03-29 Revised:2008-06-23 Online:2009-02-20 Published:2009-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10872014).

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摘要： Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.

关键词: small-world neuronal network, complete synchronization, phase synchronization, heterogeneity

Abstract: Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.

Key words: small-world neuronal network, complete synchronization, phase synchronization, heterogeneity

中图分类号:  (Neural networks and synaptic communication)

  • 87.18.Sn
05.45.Xt (Synchronization; coupled oscillators)