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Stability Analysis and Hopf-Type Bifurcation of a Fractional Order Hindmarsh-Rose Neuronal Model

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Advances in Neural Networks – ISNN 2012 (ISNN 2012)

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Abstract

In this paper, the dynamical behaviors of a fractional order Hindmarsh-Rose neuronal model are studied. First, based on the stability theory of fractional order systems, some sufficient conditions for the stability and Hpof-type bifurcation are given for such fractional order system. Then, the frequency and amplitude of periodic oscillations are determined by numerical simulations. It is shown that the frequency of oscillations incurs a small variation with respect to different values of the order, while the amplitude of oscillations gets larger as the order is increased. Numerical simulations are performed to verified the theoretical results.

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Authors and Affiliations

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

    Min Xiao

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  1. Min Xiao
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Editor information

Editors and Affiliations

  1. Department of Mechanical & Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

    Jun Wang

  2. School of Electrical and Computer Engineering, Oklahoma State University, 74078, Stillwater, OK, USA

    Gary G. Yen

  3. Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Avenue, 1678, Nicosia, Cyprus

    Marios M. Polycarpou

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© 2012 Springer-Verlag Berlin Heidelberg

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Xiao, M. (2012). Stability Analysis and Hopf-Type Bifurcation of a Fractional Order Hindmarsh-Rose Neuronal Model. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds) Advances in Neural Networks – ISNN 2012. ISNN 2012. Lecture Notes in Computer Science, vol 7367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31346-2_25

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  • DOI: https://doi.org/10.1007/978-3-642-31346-2_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31345-5

  • Online ISBN: 978-3-642-31346-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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