In the past decades, complex systems with impulsive effects and logical dynamics have received much attention in both the natural and social sciences. This historical survey briefly introduces relevant studies on impulsive differential systems (IDSs) and logical networks (LNs), respectively. To begin with, we investigate five aspects of IDSs containing fundamental theory, Lyapunov stability, input-to-state stability, hybrid impulses and delay-dependent impulses. Next, we compactly summarize the research status of some problems of LNs including controllability, stability and stabilization, observability and current research. Moreover, some significant applications of proposed results are illustrated. Finally, based on this overview, we further discuss some future work on complex systems with impulsive effects and logical dynamics.

中文翻译：

---

具有脉冲效应和逻辑动力学的复杂系统：简要概述

在过去的几十年中，具有脉冲效应和逻辑动力学的复杂系统在自然科学和社会科学中都受到了广泛的关注。这项历史调查分别简要介绍了有关脉冲差分系统（IDS）和逻辑网络（LN）的相关研究。首先，我们研究IDS的五个方面，这些方面包含基本理论，Lyapunov稳定性，输入到状态稳定性，混合脉冲和依赖于延迟的脉冲。接下来，我们简要总结了LN的一些问题的研究现状，包括可控性，稳定性和稳定性，可观察性和当前研究。此外，还说明了建议结果的一些重要应用。最后，在此概述的基础上，我们进一步讨论了对具有脉冲效应和逻辑动力学的复杂系统的一些未来工作。