In this lecture, we start by reviewing resilience concepts in complex systems and how some complex systems can suffer from large regime shifts from one discrete stable state to another. We do an analysis of the equilibria in a simple harvested fishery to motivate the "ball-in-a-basin" potential field perspective on stable states. This discussion allows us to introduce the "bifurcation diagram", which concisely summarizes the relationship between exogenous "slow" variables and the stable states of endogenous "fast" variables; this also allows us to define a "tipping point" as a bifurcation point where the equilibrium structure of the system fundamentally changes.
Whiteboard notes for this lecture can be found at: https://www.dropbox.com/s/9mq9ac000hi6j9r/SOS220-LectureC2-2023-02-02-Tipping_Points_and_Critical_Slowing_Down.pdf?dl=0
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