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Stability and Bifurcation of a Neuron Model with Delay-Dependent Parameters

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Advances in Neural Networks – ISNN 2005 (ISNN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3496))

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Abstract

An analytical method is proposed to study the dynamics of a neuron model with delay-dependent parameters. Stability and bifurcation of this model are analyzed using stability switches and Hopf bifurcation proposition. A series of critical time delay are determined and a simple stable criterion is given according to the range of parameters. Through the analysis for the bifurcation, it is shown that a very large delay could also stabilize the system. This conclusion is quite different from that of the system with only delay-independent parameters.

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References

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Author information

Authors and Affiliations

  1. College of Mathematics, Jilin University, Key Laboratory of Symbol Computation and Knowledge Engineering of Ministry of Education, 130012, Changchun, China

    Xu Xu

  2. Institute of Vibration Engineering Research, Nanjing University of Aeronautics, and Astronautics, Nanjing, 210016, China

    Xu Xu

  3. College of Computer Science and Technology, Jilin University, Key Laboratory of, Symbol Computation and Knowledge Engineering of Ministry of Education, Changchun, 130012, China

    Yanchun Liang

Authors
  1. Xu Xu
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  2. Yanchun Liang
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Editor information

Editors and Affiliations

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

    Jun Wang

  2. The Key Laboratory of Optoelectric Technology & Systems, Ministry of Education, China

    Xiaofeng Liao

  3. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

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© 2005 Springer-Verlag Berlin Heidelberg

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Xu, X., Liang, Y. (2005). Stability and Bifurcation of a Neuron Model with Delay-Dependent Parameters. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_52

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  • DOI: https://doi.org/10.1007/11427391_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25912-1

  • Online ISBN: 978-3-540-32065-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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