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Stability and Hopf bifurcation analysis on a two-neuron network with discrete and distributed delays

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  • Zhou, Xiaobing
  • Wu, Yue
  • Li, Yi
  • Yao, Xun

Abstract

In this paper, a two-neuron network with both discrete and distributed delays is considered. Local stability of this system is investigated by analyzing its associated transcendental characteristic equation. By taking the discrete time delay as a bifurcation parameter, it is found that this system undergoes a sequence of Hopf bifurcations. Moreover, formulae for determining the direction of Hopf bifurcation and the stability and period of bifurcating periodic solutions are derived. Finally, numerical simulations are given to illustrate the theoretical analysis.

Suggested Citation

  • Zhou, Xiaobing & Wu, Yue & Li, Yi & Yao, Xun, 2009. "Stability and Hopf bifurcation analysis on a two-neuron network with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1493-1505.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1493-1505
    DOI: 10.1016/j.chaos.2007.09.034
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    References listed on IDEAS

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    1. Arik, Sabri, 2005. "Global robust stability analysis of neural networks with discrete time delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1407-1414.
    2. Huang, Chuangxia & Huang, Lihong & Feng, Jianfeng & Nai, Mingyong & He, Yigang, 2007. "Hopf bifurcation analysis for a two-neuron network with four delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 795-812.
    3. Park, Ju H., 2007. "An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 800-807.
    4. Wang, Zidong & Shu, Huisheng & Liu, Yurong & Ho, Daniel W.C. & Liu, Xiaohui, 2006. "Robust stability analysis of generalized neural networks with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 886-896.
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    Cited by:

    1. Dubey, Balram & Sajan, & Kumar, Ankit, 2021. "Stability switching and chaos in a multiple delayed prey–predator model with fear effect and anti-predator behavior," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 164-192.
    2. Karaoglu, Esra & Merdan, Huseyin, 2014. "Hopf bifurcations of a ratio-dependent predator–prey model involving two discrete maturation time delays," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 159-168.

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