Personal weblog of Ted Pavlic. Includes lots of MATLAB and LaTeX (computer typesetting) tips along with commentary on all things engineering and some things not. An endless effort to keep it on the simplex.
In popular culture, words like "stochastic", "random", and "chaotic" are often used interchangeably. However, these three terms have totally different meanings. Furthermore, "randomness" and "chaos" are near opposites. Whereas "randomness" is used to simplify the process of model building, "chaos" is a phenomena that comes out of non-random models. Chaotic patterns appear random but are products of entirely deterministic processes. Chaos is an extreme sensitivity to initial conditions that relates to trajectories from deterministic systems gaining more and more individuality over time, as opposed to less. If it is chaotic, it is not random.
I explain the similarities and differences between stochasticity, randomness, and chaos in this two-part lecture recorded as a complement to material in my SOS 212 (Systems, Dynamics, and Sustainability) course at Arizona State University.
Lecture G1: Randomness and Chaos (SOS 212, Systems Dynamics and Sustainability, ASU)
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.
