Lecture Z1 (2022-04-26): Final Exam Review

This lecture reviews material for the upcoming Spring 2022 Final Exam in SOS 212. The lecture covers topics related to System Dynamics Modeling (SDM) of systems related to sustainability problems.

Lecture G1 (2022-04-14): Randomness and Chaos

In this lecture, we introduce two concepts related to the predictability of dynamical systems -- randomness and chaos. Randomness is introduced as a modeling tool to help reduce the number of dynamical variables that need to be considered to model a system. This approach is known as "stochastic modeling", where "stochastic" comes form the Greek word for "guess" or "conjecture." Stochastic modeling makes the conjecture that a system is random even if the real-world version of the system is not random but is instead complicated. Randomness simplifies model building. We then introduce chaos, which is a very strong sensitivity to initial conditions that creates deterministic behavior over time traces that appear random. We show how that chaos can be caused by (nonlinear) feedback with delay (as in the Mackey-Glass system) with as little as one state variable (stock). We then show that without delay, chaos can occur when there are 3-or-more state variables (stocks). To demonstrate this latter point, we show the Lorenz system and its corresponding Lorenz attractor (an example "strange attractor"). We discuss how the so-called "butterfly effect" relates to this extreme sensitivity to initial conditions (with Jurassic Park references).

Lecture F3 (2022-04-12): Chapter 10, Model Validity, Mental Models, and Learning (Morecroft, 2015)

In this lecture, we review the key points of Chapter 10 from Morecroft (2015), with some additional connections to literature from Frank Keil, George E.P. Box, and a few others. The chapter focuses reviews the purpose of models that fall all over the modeling spectrum -- from realistic, analog models to less realistic (but highly generalizable), simplistic, metaphorical models. We discuss how the process of building models (even simple models) helps us "transition" our mental models to more sophisticated and deeper levels of understanding and move ourselves away from the "illusion of depth" (or "shallows of explanation") that we might have before forming such models/formal theories. We extend this idea to using models to help achieve shared understanding with other experts whose expertise might differ from our own. We then pivot to discussing how we build confidence in the formal models we build -- ensuring that they have the right boundaries, structures, and equations and that they produce the right behaviors and even allows us to learn about the original system through experimenting with the modeled system.

Lecture F2 (2022-04-07): Chapter 9, Public Sector Applications of Strategic Modelling (Morecroft, 2015)

In this lecture, we discuss topics from Chapter 9 of Morecroft (2015). These topics discuss how to use system dynamics modeling in setting policies for urban growth and renewable resource management. We explore a basic model of the growth (and limits to growth) of a city before we then switch to our progressively growing model of a fishery. This fishery exhibits a "tipping point", which gives us an opportunity to discuss tipping points and bifurcation diagrams (for simulation) We then close with a discussion about how to "close the loop" in the fishery model and use modeled human behavioral responses to changes in fish density. This discussion lets us introduce policy lever as well and explore how well they might accomplish our sustainability goals.