This article focuses on the finite-time and fixed-time synchronization of a class of coupled discontinuous neural networks, which can be viewed as a combination of the Hindmarsh–Rose model and the Kuramoto model. To this end, under the framework of Filippov solution, a new finite-time and fixed-time stable theorem is established for nonlinear systems whose right-hand sides may be discontinuous. Moreover, the high-precise settling time is given. Furthermore, by designing a discontinuous control law and using the theory of differential inclusions, some new sufficient conditions are derived to guarantee the synchronization of the addressed coupled networks achieved within a finite-time or fixed-time. These interesting results can be seemed as the supplement and expansion of the previous references. Finally, the derived theoretical results are supported by examples with numerical simulations.

中文翻译：

---

耦合不连续神经网络的改进有限时间和固定时间稳定同步


本文重点研究一类耦合不连续神经网络的有限时间和固定时间同步，可以将其视为 Hindmarsh-Rose 模型和 Kuramoto 模型的组合。为此，在Filippov解的框架下，针对右侧可能不连续的非线性系统，建立了新的有限时间和定时间稳定定理。此外，还给出了高精度的稳定时间。此外，通过设计不连续控制律并利用微分包含理论，推导了一些新的充分条件，以保证所解决的耦合网络在有限时间或固定时间内实现同步。这些有趣的结果可以看作是对先前参考文献的补充和扩展。最后，得出的理论结果得到数值模拟实例的支持。