中国物理B ›› 2010, Vol. 19 ›› Issue (6): 60509-060509.doi: 10.1088/1674-1056/19/6/060509

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Phase synchronization and its transition in two coupled bursting neurons: theoretical and numerical analysis

陆启韶1, 石霞2, 王海侠3   

  1. (1)Department of Dynamics and Control\textbf{, Beihang University, Beijing 100191, China; (2)School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China; (3)School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
  • 收稿日期:2010-01-15 出版日期:2010-06-15 发布日期:2010-06-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos.~10872014 and 10802012), the Development Foundation of Science of Nanjing University of Science and Technology (Grant No.~XKF09036).

Phase synchronization and its transition in two coupled bursting neurons: theoretical and numerical analysis

Wang Hai-Xia(王海侠)a)†, Lu Qi-Shao(陆启韶)b), and Shi Xia(石霞)c)   

  1. a School of Science, Nanjing University of Science and Technology, Nanjing 210094, China; b Department of Dynamics and Control, Beihang University, Beijing 100191, China; c School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • Received:2010-01-15 Online:2010-06-15 Published:2010-06-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos.~10872014 and 10802012), the Development Foundation of Science of Nanjing University of Science and Technology (Grant No.~XKF09036).

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摘要： It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris--Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.

Abstract: It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris--Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.

Key words: phase synchronization, synchronization transition, bifurcation diagram

中图分类号:  (Neural engineering)

  • 87.85.Wc
87.18.Sn (Neural networks and synaptic communication) 87.19.L- (Neuroscience) 87.19.R- (Mechanical and electrical properties of tissues and organs) 87.19.X- (Diseases)