You are here

Introduction to Systems Analysis: Mathematically Modeling Natural Systems

Dieter M. Imboden and Stefan Pfenninger
Publication Date: 
Number of Pages: 
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
David S. Mazel
, on

When I was an electrical engineering student, my undergraduate classes were filled with circuits composed of resistors, capacitors, and inductors. From these circuits, or systems as we sometimes called them, we learned to derive linear differential equations that related voltages and currents in each of the elements. To solve the differential equations we learned Laplace Transforms. With these tools we could compute how the circuits would behave, what the voltages and currents would be in each of the elements. Of course, the behavior was always a voltage function or a current function but the modeling process was almost always the same. Such was life for an electrical engineering student.

Yet the world is not made just of circuits. Differential equations appear in more than network analysis. Indeed, the world is full of systems other than electrical networks. There are, for example, natural systems such as lakes that have an inflow and outflow; or chemical systems such as benzene in air, water; and sediment or algae growth in a lake. This book is for those who want to model these types of systems.

Imboden and Pfenninger have written a marvelous book that explores detailed systems analysis for a large variety of systems. The book gives a gentle introduction to one-parameter systems with a simple lake model. The authors are careful not to thrust too much mathematics on the reader right away but build each model from descriptive prose so that the mathematics develops naturally from the system description. This step is often missing in other books but it is crucial if readers are to understand how to analyze systems on their own.

The text shows you how to set-up the governing equations and then how to solve them. The authors discuss linear models, and time-dependent models; single variable models and multi-variable models; oscillating models with and without damping; and they even touch on non-linear models. There is a terrific chapter on chaotic models with a few predator-prey models (Lynx-Hare population deviations) and the Lorenz dynamical system. You will meet limit cycles and phase transitions.

The chapter on discrete time models is excellent as an introduction with examples of bank interest and logistic growth. Finally, the authors expand their models to time and space so readers can see that the mathematics naturally extends to multidimensional domains.

Interspersed in the book are cartoons by Nikolas Stürchler such as the one here.

The cartoons enliven the discussion and give a humorous twist to the material.

In short, this book is an excellent overview of systems analysis with varied examples and detailed explanations. It is worth having in your library.

David S. Mazel welcomes your feedback and can be contacted at mazeld at gmail dot com.