Wednesday, April 10, 2019

Bifurcation Diagrams, Hysteresis, and Tipping Points: Explanations Without Math

I teach a system dynamics modeling course (SOS 212: Systems, Dynamics, and Sustainability) at Arizona State University. It is a required course for our Sustainability BS students, which they ideally take in their second year after taking SOS 211, which is essentially Calculus I. The two courses together give them quantitative modeling fundamentals that they hopefully can make use of in other courses downstream and their careers in the future.

I end up having to cover a lot of content in SOS 212 that I myself learned through the lens of mathematics, but these students are learning it much earlier than I did and without many of the mathematical fundamentals. So I have to come up with explanations that do not rely on the mathematics. Here is an example from a recent lecture on bifurcation diagrams, hysteresis, and tipping points. It builds upon a fisheries example (from Morecroft's 2015 textbook) that uses a "Net regeneration" lookup table in lieu of a formal mathematical expression.

You can find additional videos related to this course at my SOS 212: System, Dynamics, and Sustainability playlist.


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