This paper discusses the problem of bifurcations for a delayed fractional-order neural networks (FONNs) with multiple neurons. Self-connection delay is carefully viewed as a bifurcation parameter, stability zones and bifurcation conditions are nicely established, respectively. It declares that self-connection delay immensely affects the stability and bifurcation of the developed FONNs. The explored FONNs illustrate preferable stability performance if selecting a lesser self-connection delay, and Hopf bifurcation generates once they overstep the critical values. Moreover, the effects of fractional order on the bifurcation points are fully studied. It detects that the emergence of bifurcation can be lagged as fractional order amplifies. The verification of the feasibility of the developed theory is implemented via numerical experiments.

本文讨论了具有多个神经元的延迟分数阶神经网络（FONN）的分叉问题。自连接延迟被仔细视为分叉参数，分别很好地建立了稳定区和分叉条件。它声明自连接延迟极大地影响了发达FONN的稳定性和分叉性。如果选择较小的自连接延迟，则探索的FONN会显示出较好的稳定性能，一旦超过临界值，Hopf分叉就会产生。此外，充分研究了分数阶对分叉点的影响。它检测到随着分数阶放大，分叉的出现可能会滞后。通过数值实验对开发的理论的可行性进行了验证。