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Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer’s rule

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  • Wang, Huanan
  • Huang, Chengdai
  • Liu, Heng
  • Cao, Jinde

Abstract

This article is dedicated to reseaching the bifurcations of a fractional-order neural network (FONN) with nonidentical self-connection and comunication delays. In accordance with eigenvalue analysis, we apply Cramer’s rule to ingeniously calculate the specific value of the bifurcation point of an equation set with quartic transcendence term. It is noteworthy that the method proposed in this article is more concise than the existing methods for solving higher-order transcendental terms, and has a certain degree of generalization, which can be applied to the case involving n degree transcendental terms. Furthermore, it detects that the devised FONN can ameliorate dramatically the stability attributions in comparison with its integer-order counterpart. This article ultimately provides two experimental fruits for bifurcation caused by different delays to underpin the correctness of the developed methodology.

Suggested Citation

  • Wang, Huanan & Huang, Chengdai & Liu, Heng & Cao, Jinde, 2023. "Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer’s rule," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s096007792300797x
    DOI: 10.1016/j.chaos.2023.113896
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    References listed on IDEAS

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    1. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
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    3. Song, Guang-Jing & Wang, Qing-Wen & Yu, Shao-Wen, 2018. "Cramer’s rule for a system of quaternion matrix equations with applications," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 490-499.
    4. Lin, Lifeng & Lin, Tianzhen & Zhang, Ruoqi & Wang, Huiqi, 2023. "Generalized stochastic resonance in a time-delay fractional oscillator with damping fluctuation and signal-modulated noise," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. Wang, Feng-Xian & Zhang, Jie & Shu, Yan-Jun & Liu, Xin-Ge, 2023. "On stability and event trigger control of fractional neural networks by fractional non-autonomous Halanay inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. Dai, Qinrui, 2023. "Exploration of bifurcation and stability in a class of fractional-order super-double-ring neural network with two shared neurons and multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    7. Wang, Yangling & Cao, Jinde & Huang, Chengdai, 2022. "Exploration of bifurcation for a fractional-order BAM neural network with n+2 neurons and mixed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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