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Bifurcation Control of a Fractional Order Hindmarsh-Rose Neuronal Model

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Advances in Neural Networks – ISNN 2013 (ISNN 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7952))

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Abstract

This paper proposes to use a state feedback method to control the Hopf bifurcation for a fractional order Hindmarsh-Rose neuronal model. The order of the fractional order Hindmarsh-Rose neuronal model is chosen as the bifurcation parameter. The analysis shows that in the absences of the state feedback controller, the fractional order model loses stability via the Hopf bifurcation early, and can maintain the stability only in a certain domain of the gain parameter. When applying the state feedback controller to the model, the onset of the undesirable Hopf bifurcation is postponed. Thus, the stability domain is extended, and the model possesses the stability in a larger parameter range. Numerical simulations are given to justify the validity of the state feedback controller in bifurcation control.

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Author information

Authors and Affiliations

  1. School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing, 210017, China

    Min Xiao

  2. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Min Xiao

Authors
  1. Min Xiao
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Editors and Affiliations

  1. School of Information and Communication Engineering, Dalian University of Technology, A 530, Chuangxinyuan Building, 116023, Dalian, China

    Chengan Guo

  2. Institute of Automation, Chinese Academy of Sciences, 100864, Beijing, China

    Zeng-Guang Hou

  3. School of Automation, Huazhong University of Science and Technology, 430074, Wuhan, China

    Zhigang Zeng

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Xiao, M. (2013). Bifurcation Control of a Fractional Order Hindmarsh-Rose Neuronal Model. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7952. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39068-5_11

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  • DOI: https://doi.org/10.1007/978-3-642-39068-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39067-8

  • Online ISBN: 978-3-642-39068-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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