There are several ways to define the resilience measure of a complex system. In its simplest definition, Resilience is defined as the capacity of the complex system to absorb disturbances while undergoing change as it retains essentially its function, structure, identity, and response state. In essence, in the context of climate change based water quality issues, a resilient system's water quality would be the one that would have the capacity to respond to climate change based environmental or human induced stressors without exhibiting failure modes such as uncontrollable pollution levels that would yield adverse human or ecological health effects outcome. The loss of resilience may lead to more vulnerable states in which even minor disturbances can cause a significant shift to another state that is difficult or even impossible to recover from. Thus, vulnerability is the flip side of resilience concept and occurs when a system loses its resilience and becomes vulnerable to change that previously could have been absorbed. In the context of climate change based water quality problems, the resilience concept has four components which are quantifiable using basic engineering and science based tools. These are Latitude (L), Resistance (R), Precariousness (Pr), and Panarchy (Pa). In our context Latitude is defined as the maximum amount the system can be changed before it loses its ability to recover; Resistance is the ease or difficulty of enacting a change on the system; Precariousness is the current trajectory of the complex system, and how close it currently is to a threshold which, if breached, makes the recovery difficult or impossible or moves the system to another state; Panarchy is an indicator to measure how the above three attributes are influenced by the states and dynamics of the other systems that comprise the overall complex system at scales above and below the scale of interest. In this manner, when all stressors are included, the overall system analyzed will be an integrated complex system.
Most complex systems studied in the literature in this framework include human systems as is the case with climate change based problems. Since human perception or response is an important component in the resilience methodology, the proposed models we may also include the quantifiable concept, maybe in the possibilistic sense, of adaptability and transformability. This concept is associated with a measure of the ability of a community to cope with the stress imposed on them due to a stressor in their community namely health effects of water pollution. In this sense, social resilience differs fundamentally from natural or engineered system resilience since it exhibits the capacity of humans to anticipate, adapt and plan for the future. This plays an important role in the overall evaluation of the behavior of the complex system.
The purpose of implementing this methodology would be finding ways of making desirable system basins of attraction wider and/or deeper, while shrinking undesirable states and the introduction of new stability landscapes by introducing new components. In summary, the purpose is to manage the complex system such that the overall system would work harmoniously. In essence, the analysis of stability dynamics of the linked systems of humans, environment and pollution merge from the three complementary attributes of resilience, adaptability, and transformability.
Quantification of these measures and providing a path to the analysis of system performance is not straight forward. Here we will explore the basic principles that may be used in this analysis using lower dimensional models and provide insights for higher dimensional analysis along these lines.
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