Figure 1.

The four possible responses of the equilibrium state of a system (here denoted by the state of a capital stock) to changes in an underlying, controlling variable. The equilibrium state is the amount of the capital stock that the system will eventually reach if the controlling variable is held constant at any particular level. (a) and (b) represent systems with no alternate equilibrium states; the response is smoothly changing in (a) and a step change in (b). The lateral arrows in (c) and (d) represent the direction of change. (c) and (d) involve hysteretic responses, where the return path is different from the development path, resulting in two possible stable (equilibrium) states for the same level of the controlling variable. (From Walker et al., 2009a).

 


Figure 2.

Ten interacting thresholds in the Goulburn-Broken Catchment (GB region) in South East Australia, at three scales and in three domains. The kind and magnitude of a shock will determine which threshold is most likely to be crossed, and the subsequent cascading effect through the system. Crossing one particular threshold may either increase or decrease the likelihood of another being crossed (From Walker et al., 2009b).