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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 |
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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.
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Received: 18 January 2015
Revised: 13 February 2015
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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| Fund: 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). |
Corresponding Authors:
Wei Wei
E-mail: weiweizdh@126.com
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Cite this article:
Wei Wei (魏伟), Zuo Min (左敏) Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil'nikov approach 2015 Chin. Phys. B 24 080501
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