Fuchs: Modeling of Uniform Dynamical Systems  —  Part I


There are countless ways to see, to describe, and to explain the world around us. The following pages are a very personal account of how I try to describe and explain some of the aspects which interest me most as a physicist.
The physical world and the social one created by us are systems of continuous change. This is the aspect I shall concentrate upon. For centuries, if not for thousands of years, we have tried to describe what we see, and to understand why the things work the way we see them. To this end we create models, i.e., images of the world around us. Models are our way of understanding. I shall try to introduce you to a special and particularly simple way of modeling the dynamical processes that shape the physical world and our societies. This approach is called system dynamics.
There is a simple image which goes a long way to explain—that is, to model—dynamical processes (Chapter 1). This image, which I call process thinking, assumes that processes are the result of the storage, flow, and production of certain quantities which we can imagine being some kind of imaginary “substances.” With the help of simple tools the idea is easily translated into graphical and—in the end—mathematical language. We will see how simple this is by jumping right into modeling activities. The examples lead us to think more deeply about learning and modeling, and to ask to what extent modeling can help in predicting the outcome of processes. The models are presented in detail in the accompanying CBT unit.
In Chapter 2, we will work on simple to moderately complex examples of models of processes covering different applications. The aim is to give you a feeling for how various types of dynamical behavior—exponential growth and decay, S-shaped growth, diffusive migration, overshoot and collapse, and oscillations—result from some simple model structures. Again, the models can be found in the CBT unit.

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Part I  |  Chapter 1  |  2  |  Part II