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Stability and bipartite synchronization of fractional-order coupled reaction–diffusion neural networks under unbalanced graph

Author

Listed:
  • Hao, Rixu
  • Yang, Yongqing
  • Liu, Fengyi
  • Zhou, Boling

Abstract

This paper delves into the analysis of stability and bipartite synchronization (BS) in fractional-order coupled neural networks with reaction–diffusion terms (FORDNNs) under structurally unbalanced signed graphs. Central to our investigation is the novel observation in structurally unbalanced graphs without cycles, where specific nodes under particular structures are capable of achieving BS, while others maintain stability. Subsequently, for unbalanced graphs with negative rooted cycles, we present criteria that guarantee the stability of FORDNNs. Moreover, under structurally balanced graphs, sufficient conditions for achieving BS are established. A novel approach is introduced, wherein synchronization is attained without the presence of a leader node, marking a significant departure from conventional models. Finally, illustrative examples are provided, demonstrating the effectiveness and relevance of our findings.

Suggested Citation

  • Hao, Rixu & Yang, Yongqing & Liu, Fengyi & Zhou, Boling, 2024. "Stability and bipartite synchronization of fractional-order coupled reaction–diffusion neural networks under unbalanced graph," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
  • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011354
    DOI: 10.1016/j.chaos.2024.115583
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    References listed on IDEAS

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    1. Mao, Kun & Liu, Xiaoyang & Cao, Jinde & Hu, Yuanfa, 2022. "Finite-time bipartite synchronization of coupled neural networks with uncertain parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    2. Zhu, Sha & Bao, Haibo & Cao, Jinde, 2022. "Bipartite synchronization of coupled delayed neural networks with cooperative-competitive interaction via event-triggered control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    3. Wu, Kai & Tang, Ming & Ren, Han & Zhao, Liang, 2023. "Quantized pinning bipartite synchronization of fractional-order coupled reaction–diffusion neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Lu, Jun Guo, 2008. "Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 116-125.
    5. Hebing Zhang & Xiaojing Zheng & Ning Li & Giulio E. Cantarella, 2022. "Finite-Time Pinning Synchronization Control for Coupled Complex Networks with Time-Varying Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-11, May.
    6. Li, Hong-Li & Kao, Yonggui & Hu, Cheng & Jiang, Haijun & Jiang, Yao-Lin, 2021. "Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    7. Zhang, Hai & Ye, Miaolin & Ye, Renyu & Cao, Jinde, 2018. "Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 155-165.
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