Table of Contents
- Abstract, preface, references
- 1: Introduction
- 2: Fundamentals
- 3: Examples
- 4: Findings (part 1)
- 5: Findings (part 2)
- 6: Double pendulum analysis (part 1)
- 7: Double pendulum analysis (part 2)
- 8: Double pendulum analysis (part 3)
- 9: Double pendulum analysis (part 4)
- 10: Magnetic pendulum analysis
- 11: Issues in extending finding to complex real-world systems
- 12: Real-world systems
Chapter 1. Introduction
This chapter is an overview of system dynamics, or how systems behave. To some extent its a summary of the entire book. The world is comprised of a hierarchy of systems, sub-systems and sub-sub systems. I define a system as a plurality of parts linked by natural forces such as gravity and electromagnetic, or social forces -which include economic- such that the behavior of one part affects all other parts.
The main behaviors of systems are: self-assembly (formation), oscillation (including chaotic), equilibrium (balanced forces, no movement), sudden reconfiguration (ie: chemical reactions), destruction (failure), process implementation (ie: metabolism, factory manufacturing), evolution, and reproduction.
A number of small, simple or laboratory or “toy systems” that have been extensively studied by scientists are described. These include spring-mass systems, the double pendulum, the magnetic pendulum, the Lorenz waterwheel and associated Lorenz equations, and Rayleigh-Benard convection cells. The oscillations of solar systems and molecules have also been extensively studied. Waveforms of how these systems oscillate are presented. There are links to web videos. Randomly changing or chaotic oscillations are highlighted. The butterfly effect –technically known as “sensitive dependence on initial conditions”- is analyzed in this book.
A wide range of real-world systems appear to oscillate randomly or chaotically. These include weather, planetary orbits, stock values, market shares, animal populations, and molecules. Waveforms for these are shown.
The role of energy within systems is emphasized. Basically a moving system is an energy storage device and the movement of its parts must contain or manifest the potential and kinetic energy within it. It’s found that energy can move from part to part within a system and randomly and occasionally concentrate in (or on) one part causing it to behave violently. This seems one of the very few practical and important findings from a study of chaos in multi-part systems.