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I have always understood hysteresis as that the response is depended on the way the current situation is reached, e.g. a memory effect of a magnet (knowing whether it came from a high or a low field). This might be something useful in UI as well, but I would not categorise the delay mentioned in the article as such.

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I found the first example clear: the response (which sub-menu is showing) depends on the way the current situation was reached (whether another sub-menu was showing above when you moved the mouse down and over this sub-menu).

Wikipedia defines two terms taking the possible lag into account: "Hysteresis can be a dynamic lag between an input and an output that disappears if the input is varied more slowly; this is known as rate-dependent hysteresis. However, phenomena such as the magnetic hysteresis loops are mainly rate-independent, which makes a durable memory possible." https://en.wikipedia.org/wiki/Hysteresis

That is my understanding. A good example is a light switch. if you hold a switch in the middle between on and off, you don't know which way it will snap unless you know which way the switch was moved to get to the middle.

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