中国物理B ›› 2014, Vol. 23 ›› Issue (2): 20501-020501.doi: 10.1088/1674-1056/23/2/020501

• GENERAL • 上一篇    下一篇

Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin–Huxley neuron

丁炯a, 张宏a, 童勤业a, 陈琢b   

  1. a Department of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China;
    b Department of Automation, Zhejiang University City College, Hangzhou 310015, China
  • 收稿日期:2013-04-17 修回日期:2013-05-14 出版日期:2013-12-12 发布日期:2013-12-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 60871085) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y1100119).

Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin–Huxley neuron

Ding Jiong (丁炯)a, Zhang Hong (张宏)a, Tong Qin-Ye (童勤业)a, Chen Zhuo (陈琢)b   

  1. a Department of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China;
    b Department of Automation, Zhejiang University City College, Hangzhou 310015, China
  • Received:2013-04-17 Revised:2013-05-14 Online:2013-12-12 Published:2013-12-12
  • Contact: Zhang Hong E-mail:zhangh@mail.bme.zju.edu.cn
  • About author:05.45.Pq; 05.45.Tp; 87.19.L-
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 60871085) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y1100119).

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摘要： How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin–Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional (1D) map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm – symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.

关键词: Hodgkin–, Huxley neuron, return map, symbolic dynamics, chaos

Abstract: How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin–Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional (1D) map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm – symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.

Key words: Hodgkin–Huxley neuron, return map, symbolic dynamics, chaos

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
05.45.Tp (Time series analysis) 87.19.L- (Neuroscience)