MULTIPLE STEADY STATES CREATED BY POSITIVE FEEDBACK AND THEIR EFFECTS ON SYSTEM RESPONSE TO PERTURBATION

Although intuition would lead one to assume that positive feedback, as determined by the algebraic sign of the couplings creating the feedback, must destabilize a system, this is not correct. Instead, positive feedback may either stabilize or destabilize a system and in many cases has the potential to do both depending on the state of the system at the time of perturbation. Consider, for example, the tropical forest ecosystem where positive feedback is created by couplings among leaf area index, evapotranspiration, and precipitation. A verbal assessment of the system – deforestation leads to a reduction of precipitation leading to additional loss of forest – seems to require that the feedback must destabilize the forest. However, observation, graphical analysis and mathematical models can be used to show that this is not be the case. Instead this feedback should create two steady states, one that is stable at relatively high levels of forest cover and one at lower levels that is unstable. This second steady state, a point-of-no-return for the system, separates a resilient ecosystem from one characterized by run-away behavior and system collapse. It seems likely that system behavior of this type is relatively common and may be a useful model for the investigation of catastrophic change in systems as varied as volcanic eruptions and pest populations.

It is also possible for positive feedback to produce systems with three steady states. I suggest that feedback in the global climate system created by couplings between ice and temperature is such a system. Two stable states exist separated by an unstable steady state that creates a point of bifurcation in the system. In such a system small continuous forcing like changes in solar flux during the Milankovitch cycle can be amplified to cause rapid shifts between cold and warm stable states. In fact systems that fluctuate between two relatively long-lived conditions may necessarily be controlled by positive feedback of this type. Other systems that may fit this pattern include ENSO events and shifts in lake turbidity.