The phenomenon by which the transition point between two system states depends on the direction of the transition is known as hysteresis. Hystersis is found in many natural contexts and even in M.C. Escher's drawings as explained below.
The birds at the top edge of the drawing gradually transform to fish at the bottom part. Starting at the top part and extending our view downward the transition from birds to fish occurs at the edge of the black arrow. Starting at the bottom part and extending our view upward, the transition from fish to birds occurs at the edge of the grey arrow. That is, the transition point between birds and fish depends on the direction of the transition. The reason for that is the existence of an area in the middle part of the drawing where birds and fish coexist in the sense that a white patch has a fish shape and a black patch has a bird shape. In the other two parts of the drawing there are either only birds (top) or fish (bottom).
M.C. Escher's "Sky and Water II" (c) 2005 The M.C. Escher Company - the Netherlands. All rights reserved. Used by permission. www.mcescher.com
On the relation between hysteresis and desertification read here.
