This paper considers the finite-time and fixed-time synchronization problems for the delayed inertial memristive neural networks (DIMNNs) with disturbances. Different from the existing researches, the activation functions of the investigated models are permitted to be discontinuous. In light of the Filippov solution theory and Lyapunov stability theory, a unified control strategy is designed to achieve both the goals of finite-time and fixed-time synchronization for the DIMNNs. Furthermore, some finite or fixed settling times can be expressed with different control parameters. Finally, the effectiveness of the theoretical results is illustrated by some numerical simulations, and the relationships among disturbances, controllers, and dwell time are revealed as well.

本文考虑了具有扰动的延迟惯性忆阻神经网络 (DIMNN) 的有限时间和固定时间同步问题。与现有研究不同，所研究模型的激活函数允许不连续。根据 Filippov 解理论和 Lyapunov 稳定性理论，设计了统一的控制策略来实现 DIMNN 的有限时间和固定时间同步的目标。此外，一些有限或固定的稳定时间可以用不同的控制参数来表示。最后，通过一些数值模拟说明了理论结果的有效性，并揭示了扰动、控制器和停留时间之间的关系。