Abstract In this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, the global exponential synchronization of the addressed network drive system and the response system is realized by utilizing inequality and some analysis techniques and designing the discontinuous state feedback controller. Finally, several numerical examples are given to verify the validity of the theoretical results.

中文翻译：

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具有不连续激活的混合时变延迟神经网络的全局耗散和指数同步

摘要 本文研究了具有不连续激活的非自治 Hopfield 神经网络的耗散和同步问题。首先，在扩展Filippov微分包含理论的框架下，推导出几个有效的新标准。利用广义Halanay不等式和矩阵测度方法证明了Filippov解对神经网络的全局耗散性。其次，利用不等式和一些分析技术，设计不连续状态反馈控制器，实现寻址网络驱动系统和响应系统的全局指数同步。最后给出了几个数值例子来验证理论结果的有效性。