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.
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