This paper considers the global exponential stability (GES) of high-order bidirectional associative memory (BAM) neural networks with proportional delays. Here, proportional delays are unbounded time-varying delays, which are different from constant delays, bounded time-varying delays and distributed delays. Through variable transformations, the original system can be transformed equivalently into high-order BAM neural networks with multi-constant delays and time-varying coefficients. By utilizing Brouwer’s fixed point theorem and constructing appropriate delay differential inequalities, new sufficient criteria are established to guarantee the existence, uniqueness and GES of the equilibrium point for the considered model. Finally, two examples with numerical simulations are presented to demonstrate the effectiveness of the proposed results.

中文翻译：

---

具有比例时滞的高阶双向联想记忆（BAM）神经网络的全局指数稳定性

本文考虑具有比例延迟的高阶双向联想记忆（BAM）神经网络的全局指数稳定性（GES）。在此，比例延迟是无界的时变延迟，它不同于恒定延迟，有界的时变延迟和分布式延迟。通过变量转换，原始系统可以等效地转换为具有多常数延迟和时变系数的高阶BAM神经网络。通过利用Brouwer的不动点定理并构造适当的时滞微分不等式，建立了新的充分标准来保证所考虑模型的平衡点的存在，唯一性和GES。最后，给出了两个带有数值模拟的例子，以证明所提出的结果的有效性。