AS described in Wikipedia:? "Hysteresis?is the dependence of the state of a system on its history.?Hysteresis can be a dynamic??between an input and an output that disappears if the input is varied more slowly; this is known as?rate-dependent?hysteresis.?Systems with hysteresis are?, and can be mathematically challenging to model."
An example of hysteresis in an electronic system, such as a DCC decoder, would be that the rate of change of velocity of a decoder-equipped locomotive as you move the throttle at a constant rate between minimum speed step and maximum speed step would be different when going from min to max, as compared to going from max to min.
So, to simulate physical momemtum in model railroad locomotives (which don't have very much mass compared to their real-world counterparts, and thus, not very much physical momentum), the decoder manufacturers employ "electronic hysteresis" in their model locomotives to simulate the "physical hysteresis" (a.k.a. "momentum") that is found in their Big Brothers in the real world.
And again [from Wikipedia]:? "Often, some amount of hysteresis is intentionally added to an electronic circuit to prevent unwanted rapid switching. This and similar techniques are used to compensate for??in switches, or??in an electrical signal."
