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."
Archive of lectures given as part of SOS 212 (Systems, Dynamics, and Sustainability) at Arizona State University with instructor Theodore (Ted) Pavlic.
Thursday, April 8, 2021
Lecture G1 (2021-04-08): Randomness and Chaos
Subscribe to:
Post Comments (Atom)
Popular Posts
-
In this lecture, we introduce two very different concepts – randomness and chaos. These two terms are often mistakenly used as synonyms, but...
-
In this lecture, we review the Chapter 10 of Morecroft (2015), which revisits a discussion of the function of models and discusses methods o...
-
In this lecture, we review how to simulate a the behavior over time of simple negative feedback dynamical system (the filling of water in a ...
-
In this lecture, we cover topics discussed by Morecroft (2015, Chapter 6) on the dynamics of growth and diffusion and relate them to other s...
-
In this lecture, we continue to add complexity to system dynamics models in Vensim and Insight Maker by introducing two different forms of d...
-
In this lecture, we demonstrate how to draw and simulate stock-and-flow diagrams in Insight Maker (a web-based System Dynamics Modeling (SDM...
-
In this lecture, we review the fundamentals of numerical simulation (and Euler's method) for a simple clonal bacteria population system ...
-
In this lecture, we motivate the use of causal loop diagrams (CLD's) to better understand how feedback loops interact in complex system...
-
In this lecture, we discuss how to embellish basic System Dynamics Modeling (SDM) simulation models with additional complexity and more effi...
-
This lecture reviews all content in Units A, B, C, and D in SOS 212 as preparation for the midterm. These topics cover modeling fundamental...
No comments:
Post a Comment