With the ball in the gravitational field the state of the system is entirely captured by the ball's position and velocity. With hysteresis there is some extra s

With the ball in the gravitational field the state of the system is entirely captured by the ball's position and velocity. With hysteresis there is some extra state in the system that also affects the behaviour. The general pattern you see is that if you push the system from state A to B, then from B back to A, then it will take a different path in each direction. (you can of course create mechanical systems that have this property as well, it's not specific to magnetic fields, its just that magnetic materials tend to have this kind of state-storage effect).