Hysteresis, explained.
Hysteresis is dependence of a system’s current response on its input history, so the same present input can correspond to different states.
Why it happens
Separate turn-on and turn-off thresholds create a memory band. Inside that band the input is insufficient to determine the state without knowing whether the system previously crossed one of the boundaries.
Hysteresis means a system’s current response depends on the path by which its input arrived, not only on its current input.
Read the result
Move the signal above sixty and then to fifty; the switch stays on. Move it below forty and back to fifty; it stays off. Compare the single-threshold switch, which changes solely at fifty.
A worked example
Two histories at the same input
Starting off, a signal rises from thirty to seventy and turns the switch on.
Returning to fifty leaves it on; falling to thirty turns it off, and returning to fifty leaves it off.
The identical final signal produces different states because the paths crossed different switching thresholds.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A stateful switch starts off with input 30, turns on at input >=60 and off at <=40. Inside the band it retains its state. A comparison switch uses one threshold at 50.
Where this idea is useful
A practical use
Separate switching thresholds can keep a controller from rapidly toggling when a signal jitters near one boundary.
A common misconception
“The same input must always produce the same output.”
That is true only when the response has no relevant hidden state or history. Hysteresis explicitly retains such a state.
What this explanation leaves out
- This ideal relay is an illustrative form of hysteresis, not a complete magnetic or thermal system.
How can this help with noise?
Small fluctuations within the band do not repeatedly toggle the memory switch, unlike fluctuations around a single threshold.
Where would retaining a previous state be more useful than reacting to every small fluctuation?
Further reading
Explore the original research or the teaching reference behind this experiment.