Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil'nikov approach

doi:10.1088/1674-1056/24/8/080501

中国物理B ›› 2015, Vol. 24 ›› Issue (8): 80501-080501.doi: 10.1088/1674-1056/24/8/080501

Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil'nikov approach

魏伟, 左敏

School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China

收稿日期:2015-01-18 修回日期:2015-02-13 出版日期:2015-08-05 发布日期:2015-08-05
基金资助:
Project supported by the Beijing Natural Science Foundation, China (Grant No. 4132005), the National Natural Science Foundation of China (Grant No. 61403006), the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions, China (Grant No. YETP1449), and the Project of Scientific and Technological Innovation Platform, China (Grant No. PXM2015_014213_000063).

Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil'nikov approach

Wei Wei (魏伟), Zuo Min (左敏)

School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China

Received:2015-01-18 Revised:2015-02-13 Online:2015-08-05 Published:2015-08-05
Contact: Wei Wei E-mail:weiweizdh@126.com
Supported by:
Project supported by the Beijing Natural Science Foundation, China (Grant No. 4132005), the National Natural Science Foundation of China (Grant No. 61403006), the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions, China (Grant No. YETP1449), and the Project of Scientific and Technological Innovation Platform, China (Grant No. PXM2015_014213_000063).

摘要/Abstract

摘要： In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose (HR) neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil'nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil'nikov method. The numerical simulations are performed to support the theoretical results.

关键词: Hindmarsh–, Rose neuron, Shil', nikov, chaotic motion, homoclinic orbit

Abstract: In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose (HR) neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil'nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil'nikov method. The numerical simulations are performed to support the theoretical results.

Key words: Hindmarsh–Rose neuron, Shil'nikov, chaotic motion, homoclinic orbit

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Pq (Numerical simulations of chaotic systems)

魏伟, 左敏. Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil'nikov approach[J]. 中国物理B, 2015, 24(8): 80501-080501.

Wei Wei (魏伟), Zuo Min (左敏). Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil'nikov approach[J]. Chin. Phys. B, 2015, 24(8): 80501-080501.

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Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil'nikov approach

Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil'nikov approach

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