Resilience has come to mean several different things in the system sciences.
These lectures examine the notion of ecological resilience.
For a complex system to be ecologically
resilient, one first accept system collapse as being inevitable
and then requires that the resources for subsequent system
recovery be buried in the wreckage of that collapse.
The ecological
concept of a regime shift plays an important role in enhancing a complex system's
ecological resilience. A regime shift occurs when there is an abrupt change in a system's
qualitative behavior. A system's collapse is signaled by a regime shift. But subsequent
recovery of a collapsed system is also signaled by regime shifts, thereby allowing one to achieve
ecological resilience through managed triggering of regime shifts.
These lectures
formalize the ecologist's regime shift concept by identifying regimes with components (also known as basic sets)
of a Morse decomposition of the system's chain recurrent set. This formalization allows the identification of two distinct
regime shift mechanisms; one triggered by external shocks
(shock-induced regime shift) and the other triggered by bifurcations
of the system flow (bifurcation-induced regime shift). These lectures formally define ecological resilience in terms of a discrete
abstraction (called the regime transition system) that characterizes the sequences of shock-induced regime shifts that
can be triggered in the system. These lectures show how
that transition system can be constructed from the system's
differential equation model and they demonstrate how the regime transition system can be used
to enhance ecological resilience through the careful management
of the system's regime shifts.
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