Abstract In this paper, we are concerned with the finite-/fixed-time synchronization(FFTS) problem of delayed reaction-diffusion recurrent neural networks (RNNs) with discontinuous activations. By designing a novel unified controller, with the help of theory of Filippov regularization, and a generalized finite-/fixed-time convergence theorem, we establish a threshold FFTS dynamics, which is determined by the power parameter, and the upper-bound of the settling time is explicitly estimated as well. The theoretical results herein generalize and improve some existing ones. Moreover, numerical simulations are performed to substantiate the effectiveness of the theoretical analysis.

中文翻译：

---

具有不连续激活的延迟反应扩散递归神经网络的多类型同步动力学

摘要 在本文中，我们关注具有不连续激活的延迟反应扩散递归神经网络 (RNN) 的有限/固定时间同步 (FFTS) 问题。通过设计一种新颖的统一控制器，借助 Filippov 正则化理论和广义有限/固定时间收敛定理，我们建立了阈值 FFTS 动力学，它由功率参数和稳定时间也被明确估计。本文的理论结果对现有的一些理论结果进行了概括和改进。此外，进行数值模拟以证实理论分析的有效性。