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Stability and synchronization of discrete-time fractional-order reaction–diffusion neural networks

Author

Listed:
  • Zhang, Xiao-Li
  • Yu, Yongguang
  • Wang, Hu
  • Ren, Guojian

Abstract

Discrete reaction–diffusion models have garnered considerable interest for their effectiveness in numerical simulations and their capacity to accurately reflect complex physical phenomena. Unlike traditional models, they offer a refined depiction of system dynamics across various contexts. This paper presents a pioneering investigation into the stability and synchronization of discrete-time fractional-order neural networks incorporating reaction–diffusion terms-atopic that has not been previously addressed in the literature. Leveraging Lyapunov stability theory, we derive novel global uniform asymptotic stability conditions. Furthermore, we propose new synchronization criteria based on linear state feedback control, providing a systematic framework for ensuring coordinated behavior in such networks. The effectiveness and applicability of the proposed theoretical results are validated through comprehensive numerical simulations, highlighting the practical relevance of this study.

Suggested Citation

  • Zhang, Xiao-Li & Yu, Yongguang & Wang, Hu & Ren, Guojian, 2026. "Stability and synchronization of discrete-time fractional-order reaction–diffusion neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:chsofr:v:207:y:2026:i:c:s0960077926001414
    DOI: 10.1016/j.chaos.2026.118000
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