SIAM Review, Volume 65, Issue 4, Page 1171-1184, November 2023.
A common definition of hysteresis is that the graph of the state of the system displays looping behavior as the input of the system varies. Alternatively, a dynamical systems perspective can be used to define hysteresis as a phenomenon arising from multiple equilibrium points. Consequently, hysteresis is a topic that can be used to illustrate and extend concepts in a dynamical systems course. The concept is illustrated in this paper through examples of ordinary differential equations, most motivated by applications. Simulations are presented to complement the analysis. The examples can be used to construct student exercises, and specific additional questions are listed in an appendix. The paper concludes with a discussion of possible extensions, including hysteresis in partial differential equations.

中文翻译：

---

迟滞和稳定性

SIAM Review，第 65 卷，第 4 期，第 1171-1184 页，2023 年 11 月。
滞后的常见定义是，系统状态图随着系统输入的变化而显示循环行为。或者，可以使用动态系统的视角将滞后定义为由多个平衡点引起的现象。因此，滞后是一个可用于说明和扩展动力系统课程中概念的主题。本文通过常微分方程的例子来说明这一概念，这些例子主要是受应用启发的。提出了模拟来补充分析。这些示例可用于构建学生练习，附录中列出了具体的附加问题。本文最后讨论了可能的扩展，包括偏微分方程中的滞后现象。