This paper is concerned with finite-/fixed-time synchronization for a class of Cohen–Grossberg neural networks with discontinuous or continuous activations and mixed time delays. Based on the finite-time stability theory, Lyapunov stability theory, the concept of Filippov solution and the differential inclusion theory, some useful finite-/fixed-time synchronization sufficient conditions for the considered Cohen–Grossberg neural networks are established by designing two kinds of novel periodically switching controllers. Instead of using uninterrupted high control strength, the periodically switching controller in each period is used with high strength control in one stage and weak strength in the other. It can overcome the effects caused by the uncertainties of Filippov solution induced by discontinuous neuron activation functions and reduce the control cost. Besides, the period switching control rate is closely related to the settling time T. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of the obtained results.

本文关注具有不连续或连续激活和混合时间延迟的一类 Cohen-Grossberg 神经网络的有限/固定时间同步。基于有限时间稳定性理论、Lyapunov 稳定性理论、Filippov 解的概念和微分包含理论，通过设计两种可用的 Cohen-Grossberg 神经网络，建立了一些有用的有限/固定时间同步充分条件。新颖的周期性切换控制器。不是采用不间断的高控制强度，而是采用每个周期的周期性切换控制器，一个阶段控制强度高，一个阶段控制强度弱。它可以克服由不连续的神经元激活函数引起的 Filippov 解的不确定性带来的影响，降低控制成本。此外，周期开关控制率与建立时间密切相关吨。最后通过两个数值算例证明了所得结果的有效性和可行性。