This work is chiefly concerned with the stability behavior and the appearance of Hopf bifurcation of fractional-order delayed Cohen–Grossberg neural networks. Firstly, we study the stability and the appearance of Hopf bifurcation of the involved neural networks with identical delay . Secondly, the sufficient criterion to guarantee the stability and the emergence of Hopf bifurcation for given neural networks with the delay is set up. Thirdly, we derive the sufficient condition ensuring the stability and the appearance of Hopf bifurcation for given neural networks with the delay . The investigation manifests that the delay plays a momentous role in stabilizing networks and controlling the Hopf bifurcation of the addressed fractional-order delayed neural networks. At last, software simulation results successfully verified the rationality of the analytical results. The theoretical findings of this work can be applied to design, control, and optimize neural networks.

中文翻译：

---

包含时滞的分数阶Cohen-Grossberg神经网络的分歧研究

这项工作主要涉及分数阶延迟Cohen-Grossberg神经网络的稳定性和Hopf分叉的出现。首先，研究具有相同时滞的相关神经网络的Hopf分叉的稳定性和出现。。其次，对于给定时滞的神经网络，有充分的准则可以保证Hopf分叉的稳定性和出现。设置好了。第三，对于给定的时滞神经网络，我们推导出了确保Hopf分叉的稳定性和出现的充分条件。。研究表明，延迟在稳定网络和控制寻址的分数阶延迟神经网络的Hopf分支方面起着重要作用。最后，软件仿真结果成功验证了分析结果的合理性。这项工作的理论发现可以应用于设计，控制和优化神经网络。