This paper formulates new theoretical results concerning the multiple $O\left(t^{-q}\right)$ stability and instability for a class of time-varying delayed fractional-order Cohen-Grossberg neural networks (FoCGNNs) with Gaussian activation functions. With the aid of geometrical configurations obtained from the FoCGNNs model and Gaussian functions, the state space are partitioned into $3^k$ subspaces, where k is a nonnegative constant determined by the parameters of FoCGNNs model. By means of the Brouwer’s fixed point theorem as well as the contraction mapping, it is guaranteed that there exists a unique equilibrium point in each subspace. Sufficient conditions are achieved that $2^k$ equilibrium points are locally $O\left(t^{-q}\right)$ stable and $3^k-2^k$ equilibrium points are unstable. Several examples are rendered to demonstrate the feasible analysis of the theoretical results.

本文针对多重性提出了新的理论结果 $Ø（{Ť}^{--q}）$一类具有高斯激活函数的时变时滞分数阶Cohen-Grossberg神经网络（FoCGNNs）的稳定性和不稳定性。借助从FoCGNNs模型和高斯函数获得的几何构型，将状态空间划分为$3^{ķ}$子空间，其中k是由FoCGNNs模型的参数确定的非负常数。通过Brouwer的不动点定理和收缩映射，可以确保在每个子空间中都有一个唯一的平衡点。达到了足以满足以下条件的条件${\mathrm{2个}}^{ķ}$ 平衡点是局部的 $Ø（{Ť}^{--q}）$ 稳定且 $3^{ķ}--{\mathrm{2个}}^{ķ}$平衡点不稳定。给出了几个例子来证明对理论结果的可行性分析。