This article investigates the problem of relaxed exponential stabilization for coupled memristive neural networks (CMNNs) with connection fault and multiple delays via an optimized elastic event-triggered mechanism (OEEM). The connection fault of the two or some nodes can result in the connection fault of other nodes and cause iterative faults in the CMNNs. Therefore, the method of backup resources is considered to improve the fault-tolerant capability and survivability of the CMNNs. In order to improve the robustness of the event-triggered mechanism and enhance the ability of the event-triggered mechanism to process noise signals, the time-varying bounded noise threshold matrices, time-varying decreased exponential threshold functions, and adaptive functions are simultaneously introduced to design the OEEM. In addition, the appropriate Lyapunov–Krasovskii functionals (LKFs) with some improved delay-product-type terms are constructed, and the relaxed exponential stabilization and globally uniformly ultimately bounded (GUUB) conditions are derived for the CMNNs with connection fault and multiple delays by means of some inequality processing techniques. Finally, two numerical examples are provided to illustrate the effectiveness of the results.

中文翻译：

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通过优化的弹性事件触发机制实现具有连接故障和多重延迟的耦合忆阻神经网络的宽松指数稳定

本文通过优化的弹性事件触发机制 (OEEM) 研究具有连接故障和多重延迟的耦合忆阻神经网络 (CMNN) 的松弛指数稳定问题。两个或部分节点的连接故障会导致其他节点的连接故障并引起CMNN的迭代故障。因此，考虑采用备份资源的方法来提高CMNN的容错能力和生存能力。为了提高事件触发机制的鲁棒性，增强事件触发机制处理噪声信号的能力，同时引入时变有界噪声阈值矩阵、时变递减指数阈值函数和自适应函数设计 OEM。此外，构造了具有一些改进的延迟乘积类型项的适当的 Lyapunov-Krasovskii 泛函（LKF），并通过一些方法导出了具有连接故障和多个延迟的 CMNN 的松弛指数稳定和全局一致最终有界（GUUB）条件不等式处理技术。最后，提供两个数值例子来说明结果的有效性。