Threshold is represented by contour lines (of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value) which is considered the breakpoint or tipping point between two or more regimes, levels in underlying controlling variables of a system in which feedbacks to the rest of the system changes, the change in dynamics is sudden while the change in observable variables can be slow or fast. Threshold gradient represents that limit whereby system set of states or configurations are possible and from 3 dimensional perspective may have different heights that lead to different regimes.
When a threshold along a controlling variable in a system is passed, the nature and extent of feedbacks change, such that there is a change in the direction in which the system moves. A shift occurs when internal processes of the system (rates of birth, mortality, growth, consumption, decomposition, leaching, etc.) have changed such that the variables that define the state of the system begin to change in a different direction, towards a different attractor. In some cases, crossing the threshold brings about a sudden, large and dramatic change in the responding variables, whilst in other cases the response in the state variables is continuous and more gradual.
The threshold levels (tipping point) indicate the natural progression of a system to different basin of attraction (regime). Some consideration with respect to thresholds:
- Systems are complex adaptive systems that may have multiple basins of attraction and limited predictability
- When crossed thresholds between multiple basins of attraction can lead to fundamental transformations in system feedbacks and dynamics
- Managing resilience specifically recovery from disturbance is important, even more important the focus on threshold boundaries that may have major consequences to performance potential when crossed
- Thresholds can be used to screen or rule out actions that have a high risk of crossing into unfavorable basin; recovery in certain cases might require extreme effort and resources
- Resilience engineering focuses on critical thresholds for system performance, if current basin (current situation is desirable) then govern the system towards increasing resilience, build capacity to recognize and respond emerging conditions/disturbances before they occur and finally build capacity to adapt should transformation occur.
- Systems trajectory dynamics tend to move towards least favorable basin
Disturbances can cause system state to shift ‘trajectory a‘ and either remain within resilience threshold or its resilience threshold is overwhelmed (resilience tipping point) ‘trajectory b’ moving to a new resilience threshold as shown in system ‘trajectory c’ which has totally different function, structure, identity, and feedback. Current system sates with its potential/performance can either be superior or inferior to previous system state: all depending on the resilience threshold.