中国物理B ›› 2005, Vol. 14 ›› Issue (1): 77-85.doi: 10.1088/1009-1963/14/1/016

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Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons

石霞, 陆启韶   

  1. School of Science, Beijing University of Aeronautics and Astronautics,Beijing,100083, China
  • 收稿日期:2004-04-21 修回日期:2004-09-02 出版日期:2005-01-20 发布日期:2005-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10432010) and the Doctoral Research Foundation of Beijing University of Aeronautics and Astronautics.

Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons

Shi Xia (石霞), Lu Qi-Shao (陆启韶)   

  1. School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2004-04-21 Revised:2004-09-02 Online:2005-01-20 Published:2005-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10432010) and the Doctoral Research Foundation of Beijing University of Aeronautics and Astronautics.

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摘要： The firing activities of Hindmarsh--Rose (HR) neurons are studied by means of numerical simulation and bifurcation analysis.A single HR neuron exhibits various firing patterns, such as quiescent state, periodic spiking, periodic bursting and chaos,when the external current input is changed. The fast/slow dynamical analysis is applied to explore the dynamical behaviour of the HR model. The complete synchronization of two coupled identical HR neurons with electrical coupling mimicking gap junctions can be realized in certain ranges of the coupling strength, whenever each individual neuron shows quiescency,periodic firing and chaos. The criteria for complete synchronization are analysed theoretically, and the corresponding numerical simulation is presented as well. The persistence of the interspike intervals bifurcation structure of the coupled HR neuronal system under electrical coupling is also discussed.

关键词: Hindmarsh--Rose neuron, synchronization, coupling, gap junction

Abstract: The firing activities of Hindmarsh--Rose (HR) neurons are studied by means of numerical simulation and bifurcation analysis.A single HR neuron exhibits various firing patterns, such as quiescent state, periodic spiking, periodic bursting and chaos,when the external current input is changed. The fast/slow dynamical analysis is applied to explore the dynamical behaviour of the HR model. The complete synchronization of two coupled identical HR neurons with electrical coupling mimicking gap junctions can be realized in certain ranges of the coupling strength, whenever each individual neuron shows quiescency,periodic firing and chaos. The criteria for complete synchronization are analysed theoretically, and the corresponding numerical simulation is presented as well. The persistence of the interspike intervals bifurcation structure of the coupled HR neuronal system under electrical coupling is also discussed.

Key words: Hindmarsh--Rose neuron, synchronization, coupling, gap junction

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  • 0545