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

doi:10.1088/1674-1056/23/2/020501

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.

Keywords: Hodgkin–Huxley neuron return map symbolic dynamics chaos

Received: 17 April 2013
Revised: 14 May 2013
Accepted manuscript online:

PACS:	05.45.Pq	(Numerical simulations of chaotic systems)
	05.45.Tp	(Time series analysis)
	87.19.L-	(Neuroscience)

Fund: 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).

Corresponding Authors: Zhang Hong
E-mail: zhangh@mail.bme.zju.edu.cn

About author: 05.45.Pq; 05.45.Tp; 87.19.L-

Cite this article:

Ding Jiong (丁炯), Zhang Hong (张宏), Tong Qin-Ye (童勤业), Chen Zhuo (陈琢) Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin–Huxley neuron 2014 Chin. Phys. B 23 020501

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

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