In this paper, two multiple weighted coupled reaction–diffusion neural networks (CRDNNs) with and without coupling delays are introduced. On the one hand, some finite-time passivity (FTP) concepts are proposed for the spatially and temporally system with different dimensions of output and input. By choosing appropriate Lyapunov functionals and controllers, several sufficient conditions are presented to ensure the FTP of these CRDNNs. On the other hand, the finite-time synchronization (FTS) problem is also discussed for the multiple weighted CRDNNs with and without coupling delays, respectively. Finally, two numeral examples with simulation results are provided to verify the effectiveness of the obtained FTP and FTS criteria.

中文翻译：

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多权重耦合反应扩散神经网络的有限时间无源性与同步

在本文中，介绍了带有和不带有耦合时延的两个多重加权耦合反应扩散神经网络（CRDNN）。一方面，针对具有不同输出和输入维度的时空系统，提出了一些有限时间无源（FTP）概念。通过选择适当的Lyapunov功能和控制器，可以提供几个充分的条件来确保这些CRDNN的FTP。另一方面，还分别讨论了具有和不具有耦合延迟的多重加权CRDNN的有限时间同步（FTS）问题。最后，提供了带有仿真结果的两个数字示例，以验证所获得的FTP和FTS标准的有效性。