In this lecture, we introduce the concepts of stochastic modeling (the use of randomness to simplify the modeling process) and chaos (the extreme sensitivity to initial conditions that makes deterministic systems appear to be random. To demonstrate stochastic modeling, we develop a discrete event system simulation model of a bacterial population. This gives an opportunity to discuss random number generation/random number streams and how they allow non-random computers to approximate randomness and realistic variation (allowing for realistic experimentation). We pivot to discussing chaos -- using the Mackey-Glass and Lorentz systems as key examples (one that has a single stock with delay in the flow, the other that has three stocks with simple flows). We finish by connecting these results to the so-called "butterfly effect."
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