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<p>In this article, we study the stability and bifurcations of a fractional-order neutral neural network with three types of delays. A four-dimensional fractional-order neutral-type neural network (FONTNN) is firstly established. Secondly, the bifurcation results of the proposed FONTNN are extracted by the analytical method of characteristic equations and Cramer’s rule. It demonstrates that FONTNN can neatly improve the performance stability of the system in comparison with integer-order neural networks. Moreover, the influence of fractional orders is nicely explored. It discovers that the bifurcation points extremely depend on fractional orders. The stability performance can be adjusted by selecting some appropriate fractional orders. The authenticity of the developed theoretical outcomes is ultimately corroborated through numerical simulations.</p>

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Bifurcations of a fractional-order neutral-type neural network

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Chengdai Huang,
  • Jin Ban,
  • Naif D. Alotaibi,
  • Mahmoud Abdel-Aty,
  • Jinde Cao

摘要

In this article, we study the stability and bifurcations of a fractional-order neutral neural network with three types of delays. A four-dimensional fractional-order neutral-type neural network (FONTNN) is firstly established. Secondly, the bifurcation results of the proposed FONTNN are extracted by the analytical method of characteristic equations and Cramer’s rule. It demonstrates that FONTNN can neatly improve the performance stability of the system in comparison with integer-order neural networks. Moreover, the influence of fractional orders is nicely explored. It discovers that the bifurcation points extremely depend on fractional orders. The stability performance can be adjusted by selecting some appropriate fractional orders. The authenticity of the developed theoretical outcomes is ultimately corroborated through numerical simulations.