Fig. 5. Relaxing the monotonic assumption of the relation between conditions and state of the system. The red and blue parts of the curve represent the location of stable points, and the red and blue lines near the abscissa represent the basins of attraction for the two stable point configurations, according to either red or blue.

a. Possibility of catastrophic shift in syndrome resulting from a small change in conditions, due to the basic hysteretic framework. If the system is located at either of the initial positions of either of the arrows, a very slight change in the conditions will result in a sudden shift of the system from one syndrome to the other.

b. Possibility of sudden change in syndrome due to basin boundary collision, or the crossing of a basin separatrix through stochastic processes (the red shading indicates the zone of chaotic or quasiperiodic behavior or stochastic variation). If the red zone intersects the edge of the part of the curve that bends over, eventually the system will jump from one syndrome to the other. Note that this kind of jump does not require any change in the conditions at all.

Fig. 5