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Stability and bifurcation control of a neuron system under a novel fractional-order PD controller

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  • Special Topic: Nonlinear Dynamics and Control
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Abstract

In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative (PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally, numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.

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Authors and Affiliations

  1. School of Automation, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Shuo Shi, Min Xiao, LiNa Rong, BinBin Tao & FengYu Xu

  2. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, China

    Min Xiao & ZunShui Cheng

  3. School of Computing, Engineering and Mathematics, Western Sydney University, Penrith, NSW, 2751, Australia

    WeiXing Zheng

Authors
  1. Shuo Shi
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  2. Min Xiao
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  3. LiNa Rong
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  4. WeiXing Zheng
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  5. BinBin Tao
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  6. ZunShui Cheng
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  7. FengYu Xu
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Corresponding author

Correspondence to Min Xiao.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61573194, 51775284), the Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK20181389, BK20171441), the Key Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province (Grant No. 2018SJZDI142), and the Australian Research Council (Grant No. DP120104986).

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Shi, S., Xiao, M., Rong, L. et al. Stability and bifurcation control of a neuron system under a novel fractional-order PD controller. Sci. China Technol. Sci. 62, 2120–2129 (2019). https://doi.org/10.1007/s11431-018-9496-x

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  • DOI: https://doi.org/10.1007/s11431-018-9496-x

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