SOS 212: Systems, Dynamics, and Sustainability

Lecture Z1 (2022-11-29): Final Exam Review

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 29 Nov 2022 19:14:00 -0700

In this lecture, we prepare for the final exam and review topics from the whole semester.

Lecture G1 (2022-11-17): Randomness and Chaos

ted@tedpavlic.com (Theodore P. Pavlic) — Fri, 18 Nov 2022 10:56:00 -0700

In this lecture, we introduce two very different concepts – randomness and chaos. These two terms are often mistakenly used as synonyms, but they are far from it.

We introduce randomness as a modeling tool that helps us make sense of the world and reduce the complexity of models that we use to describe the world. This approach – using randomness to simplify descriptions of otherwise very complicated small-scale behavior – is called "stochastic modeling." "Stochastic" here comes from the Greek for guessing or conjecturing, thus exposing that "stochastic" is not a synonym for randomness but is actually an approach for assuming randomness even when there is no reason to believe that randomness is actually playing a role in the "real" system. We then describe how to use numerical approximations of randomness (from mathematical functions implemented within a computer) to generate stochastic computer simulation models within Vensim and Insight Maker. Traditionally, these kinds of models would be built within "Discrete Event System simulation" tools (like Arena or AnyLogic or others), but we show how our system dynamics modeling (SDM) tools can be co-opted to have random outputs too.

We then pivot away from randomness to describe chaos, which is an extreme sensitivity to initial conditions that can be present in even very simple single-stock system dynamics models (so long as they have delay and nonlinear feedback). This extreme sensitivity to initial conditions often leads to behavior-over-time plots that appear to be random even though they are determined entirely by the internal state of the system (i.e., they are "locally predictable"). We demonstrate this with the Mackey–Glass system. We then show how chaos can emerge without delay in systems with three (or more) stocks, and this is demonstrated with the Lorenz system. By plotting the three stocks against each other, we can see that the apparently random behavior-over-time plots actually have structure, which is captured by the "Lorenz attractor", an example "strange attractor" in chaotic systems. We use this new understanding of chaos to better explain the popularized "butterfly effect", which is NOT about butterflies "causing" weather events but more about how a universe with a butterfly in one position might unroll very differently than a universe with a butterfly in a different position.

So, randomness is a tool we use to make models simpler (or have fewer variables and parameters), and chaos is a tricky phenomenon that makes modeling and analysis harder.

Lecture F3 (2022-11-15): Chapter 10, Model Validity, Mental Models, and Learning (Morecroft, 2015)

ted@tedpavlic.com (Theodore P. Pavlic) — Wed, 16 Nov 2022 15:47:00 -0700

In this lecture, we review the Chapter 10 of Morecroft (2015), which revisits a discussion of the function of models and discusses methods of building confidence in (simulation) models. We connect Morecroft's message to similar messages from Frank Keil (on formal models/theories and the shallows of explanation). We also discuss how tangible models that Morecroft describes as "transitional objects" can also be viewed as "boundary objects" on interdisciplinary teams. We discuss different ways of verifying, validating, and calibrating models. This lets us discuss things like boundary adequacy and structural adequacy, which are important to designing the high-level architecture of a model. We close with a discussion of how ultimately we build the most confidence in models when those models result in us learning something about a system.

Lecture F2 (2022-11-10): Chapter 9, Public Sector Applications of Strategic Modelling (Morecroft 2015)

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 10 Nov 2022 19:31:00 -0700

In this lecture, we review topics from Chapter 9 of Morecroft (2015) on public sector applications of strategic modelling (i.e., system dynamics modeling, SDM). We start by walking through Forrester's Urban Growth Dynamics model and how it helps act as a lens for thinking about the drivers of stagnation in cities. Then we shift to thinking about regulation in a fishery. We take this opportunity to introduce the notion of a "tipping point" as well as the tool of a "bifurcation diagram." We do not have enough time to show how to endogenize exploitation decisions within the fishery model, but details of this are presented by Morecroft (2015).

Lecture F1 (2022-11-04): Chapter 8, Industry Dynamics – Oil Price and the Global Oil Producers (Morecroft, 2015)

ted@tedpavlic.com (Theodore P. Pavlic) — Fri, 4 Nov 2022 12:52:00 -0700

In this lecture, we cover examples and a case study explored by Morecroft (2015, ch. 8) relating to building and using system dynamics models of the global oil industry. At a high level, the salient points are how to model an apparently large and complex system with a tractable set of (relatively small) stocks and how to build models sector by sector to reduce the modeling burden. At a lower level, we focus on modeling the effects of OPEC (Organization of Petroleum Exporting Countries) on the global oil industry.

Lecture E5 (2022-10-27): Assignment E5 – Creating Limited, Coupled Population Models

ted@tedpavlic.com (Theodore P. Pavlic) — Fri, 28 Oct 2022 16:07:00 -0700

In this lecture, we discuss an upcoming assignment in SOS 212 that will provide practice in creating more complex, multi-sector system dynamics models. We review how to create rate formulas for processes like population growth. We review lookup tables. We review ghost primitives/shadow variables. We also introduce how to use modular arithmetic (mod/modulo/modulus) that, when combined with a lookup table, makes seasonal patterns easy to introduce in system dynamics models. This is also covered for both Vensim (from Ventana Software) and Insight Maker.

Lecture E4 (2022-10-25): Chapter 6, The Dynamics of Growth and Diffusion (Morecroft, 2015)

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 25 Oct 2022 21:18:00 -0700

In this lecture, we cover topics discussed by Morecroft (2015, Chapter 6) on the dynamics of growth and diffusion and relate them to other systems with S-shaped growth that we've seen in the past – a simple fishery model as well as epidemic growth. The main focus of this chapter is on the Bass model of innovation diffusion, which includes a contagion-like word-of-mouth loop (similar to the "SI" in an "SIR" model, or similar to population growth in a fishery) as well as an advertising loop to get the process started (like inoculating a population with its first infectious individuals). We then cover embellishments of the Bass model and do a strategic thinking example on one of those embellishments, which relates to strategy for the entry of easyJet as a low-cost airline into an existing marketplace of major carriers.

Lecture E3 (2022-10-20): Epidemic Dynamics

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 20 Oct 2022 19:19:00 -0700

In this lecture, we start to introduce more complex system dynamics models (SDM), as would be implemented in Vensim or Insight Maker, for more complex systems. We focus on the classical SIR (susceptible–infectious–recovered) multi-compartment model from epidemiology. We build up this model as a stock-and-flow diagram from scratch, justifying the expressions/equations that we use and then using simulation to inform us when the equations might have significant flaws. Ultimately, we get to a working SIR model that matches dynamics of basic disease spread, and we go through a strategic thinking/scenario-planning example that shows that the value of quarantine policy is, in most cases, not to reduce spread of a disease but "flatten the curve" and lower (but widen) the infection peak to keep it under a manageable public-health threshold (set by university capacity/etc.).

Lecture E2 (2022-10-18): Making Simulations More Realistic, Part 2 – Delays, Fixed and Smoothing

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 18 Oct 2022 20:37:00 -0700

In this lecture, we continue to add complexity to system dynamics models in Vensim and Insight Maker by introducing two different forms of delays – fixed delays and smoothing/averaging delays. We spend some of the lecture discussing the fundamental difference between these delays, and we spend much of the rest of the lecture discussing how to implement these delays in both Vensim and Insight Maker. We also discuss some other functions (like STEP, for step responses, and PULSE/PULSE TRAIN) as well as how to use lookup tables to insert more arbitrary functions over time as inputs to systems. Finally, we spend some time discussing how higher-order smoothing/averaging delays help mix aspects of both fixed delays and pure smoothing delays.

Lecture E1 (2022-10-14): Making Simulations More Realistic, Part 1 – Units, Sliders, and Lookup-Table Converters

ted@tedpavlic.com (Theodore P. Pavlic) — Fri, 14 Oct 2022 12:53:00 -0700

In this lecture, we discuss how to embellish basic System Dynamics Modeling (SDM) simulation models with additional complexity and more efficiently interact with working simulation models. In particular, we introduce units (in both Vensim and Insight Maker) as a tool for the verification and validation of simulation models. We also discuss how to use sliders (in both Vensim and Insight Maker) to quickly adjust parameters (constants) and generate new outputs. We close with a discussion of lookup tables (converters) as well as how to implement them in both Vensim and Insight Maker.

Lecture D-E (2022-09-29): Midterm Review

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 29 Sep 2022 19:32:00 -0700

Midterm review session for ASU SOS 212 for Fall 2022.

Lecture D4 (2022-09-27): Chapter 3, Modelling Dynamic Systems (Morecroft, 2015)

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 27 Sep 2022 21:33:00 -0700

In this lecture, we demonstrate how to draw and simulate stock-and-flow diagrams in Insight Maker (a web-based System Dynamics Modeling (SDM) tool), and then we discuss the third chapter of Morecroft (2015), which introduces the reader to stock-and-flow diagrams and numerical simulations of dynamical systems. We go through a simple example modeling the flows of instructors into and out of a university, and then we move to a more complex multi-sector simulation of a community attempting to regulate drug use through the use of police. This latter simulation helps illustrate how to form equations for flows and converter variables, and it also demonstrates how anomalous behaviors that are generated by simulations can help indicate where problems may be in simulation formulas (which should then be updated to make the simulation outputs more realistic).

Lecture D3 (2022-09-23): Stock-and-Flow Diagrams in Vensim and Insight Maker

ted@tedpavlic.com (Theodore P. Pavlic) — Fri, 23 Sep 2022 10:20:00 -0700

In this lecture, we start by reviewing numerical integration methods (Euler's method) for approximating solutions to ordinary differential equations in spreadsheets. We use a filling toilet tank as an example of a balancing/negative-feedback system that we can simulate this way. We then pivot to discussing stock-and-flow diagram representations of these systems and then end with a short demonstration about how to use Vensim to draw and simulate these stock-and-flow diagrams, thereby greatly accelerating the numerical integration process done by hand in the spreadsheet. We ran out of time before being able to cover the example in Insight Maker, but we will start with that at the beginning of the next lecture.

Lecture D2 (2022-09-20): Introduction to Numerical Simulation of Dynamical Systems, Part 2

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 20 Sep 2022 18:28:00 -0700

In this lecture, we review the fundamentals of numerical simulation (and Euler's method) for a simple clonal bacteria population system with only births. We then add a death flow in and explore how changing the numerical simulation time step ("dt") affects the results. We then transition to a numerical simulation of a toilet tank (a classic balancing feedback loop).

Lecture D1 (2022-09-15): Introduction to Numerical Simulation of Dynamical Systems, Part 1

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 15 Sep 2022 23:25:00 -0700

In this lecture, we introduce numerical simulation of dynamical systems (coupled ordinary differential equations) within the context of stock-and-flow diagrams for System Dynamics Modeling in strategic thinking. After covering how systems of ODE's capture the underlying "forces" driving change in a system, we review different ways to think about compound interest. This compound interest example motivates "Euler's method" for numerical integration over time. That is, we describe the product of flows and time-step durations as a sort of "interest" earned over each simulation time step ("compounding period" in the bank analogy). We use a bacterial growth example to show how this perspective can let us simulate the (average) growth characteristics of a bacterial population without having to simulate the discrete events where each bacteria reproduces independent of each other bacteria. Overall, this lecture relates the "time step" parameter in tools like Vensim and Insight Maker to calculus-based topics like the definition of the derivative. Furthermore, this lecture uses spreadsheet tools (like Microsoft Excel and Google Sheets) to provide a picture of what goes on inside simulation tools like Vensim and Insight Maker.

Lecture C2 (2022-09-13): "Applying Systems Archetypes" (Kim and Lannon, 1997)

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 13 Sep 2022 21:25:00 -0700

In this lecture, we review the perspectives of Kim and Lannon (1997) toward applying Systems Archetypes in strategic modeling. This involves four approaches – structural pattern templates, lenses, dynamical theories, and predicting future behavior – that capture most of the different ways that Systems Archetypes can be used to propose interventions (or predict hypothetical outcomes from those interventions) in the iterative process of using models to make changes in the world.

Lecture C1 (2022-09-08): Feedback Systems Thinking with CLDs

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 8 Sep 2022 21:56:00 -0700

In this lecture, we start to introduce "systems archetypes" as representing more complex aggregations of loops that give rise to complex (but predictable) behaviors over time. We introduce S-shaped growth as a modification to reinforcing loops, balancing loops with delay as a modification to balancing loops, and growth with overshoot as a combination of the two. We then expose several of the other more complex archetypes as an introduction to the upcoming article on using systems archetypes in the next lecture. The lecture experience closes with groups working on building their own S-shaped growth examples and "shifting goals" examples.

Lecture B3 (2022-09-06): Chapter 2, Introduction to Feedback Systems Thinking (Morecroft, 2015)

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 6 Sep 2022 18:44:00 -0700

In this lecture, we review Chapter 2 (Introduction to Feedback Systems Thinking) from Morecroft (2015). This chapter contrasts event-driven thinking with feedback systems thinking, which are two perspectives on analyzing possible interventions in the world. The former focuses on reacting to problems as they occur, with their causes (as well as the long-term intervention consequences) being outside of the decision-making model. The latter focuses on considering not only the intervention but the possible side effects related to other dynamic forces that are distal from the main problem of interest. A focal road congestion example is used throughout, with the chapter closing on an example about dueling showers ("accidental adversaries") and how they can be viewed as a model for dueling sub-units of a single company with limited capacity to operate both simultaneously.

Lecture B2 (2022-09-01): Drawing Causal Loop Diagrams in Vensim

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 1 Sep 2022 19:45:00 -0700

In this lecture, we review causal loop diagram (CLD) fundamentals and go through a few examples of building and annotating CLDs. We also go over how to draw CLD's in the Vensim PLE system dynamics modeling tool.

Note that due to atypical technological limitations in the classroom at the time of the recording, the video quality is not optimal.

Lecture B1 (2022-08-30): Introduction to Causal Loop Diagrams

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 30 Aug 2022 18:49:00 -0700

In this lecture, we motivate the use of "causal loop diagrams" as a bridge for building system dynamics models as well as analyzing models already built. We then introduce the fundamental structures within CLDs – the links (positive and negative, with and without delays) and the feedback loops (positive/reinforcing and negative/balancing/counteracting/regulating, and annotations denoting polarity as well as application-specific context). We do a few examples of drawing and analyzing simple CLD's and discuss rules and conventions for choosing variables to include in CLD's.

Lecture A3 (2022-08-25): Chapter 1, The Appeal and Power of Strategic Modeling (Morecroft, 2015)

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 25 Aug 2022 19:02:00 -0700

In this lecture, we discuss topics from Chapter 1 of Morecroft (2010) surrounding strategic modeling for analysis of various different scenarios that can emerge from a single system dynamics model. After some philosophical discussion of the continuous modeling spectrum from metaphorical to analog, we transition to more concrete examples with a simple harvested fisheries model. This gives us the opportunity to use the SDM to show how important functional response is and to use the example to motivate approaches for regulating a sustainable fishery.

Lecture A2 (2022-08-23): Introduction to Modeling

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 23 Aug 2022 18:25:00 -0700

In this lecture, we introduce modeling broadly, including the different types of models (mental models, physical models, animal models, mathematical/analytical models, computational/numerical models, and simulation models) and how they are used. We focus on how modeling is as much about leaving the right things out as it is choosing the right things to keep in.

Lecture A1 (2022-08-18): Course Introduction

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 18 Aug 2022 21:23:00 -0700

Introduction to the course and the start of an introduction to quantitative simulation modeling.

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

ted@tedpavlic.com (Theodore P. Pavlic) — Tue, 26 Apr 2022 19:53:00 -0700

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

ted@tedpavlic.com (Theodore P. Pavlic) — Thu, 14 Apr 2022 17:01:00 -0700

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).