An Introduction to Complex Systems

Paul Fieguth


Table of Contents (see also List of Examples, Link to Chapters 1/2 (PDF))

The chapters of the text are intended to be read in sequence, although the case studies and examples are designed to be relatively stand-alone and accessible to most readers.

The text aims to be mathematically clear and rigorous, but emphasizing high-level concepts and effects.

Click on the bold chapter headings below to expand / collapse chapter section/subsection details:

Chapter 1: Introduction:

1.1 How to Read This Text
References

Chapter 2: Global Warming and Climate Change

Further Reading
References

Chapter 3: Systems Theory

3.1 Systems and Boundaries
3.2 Systems and Thermodynamics
3.3 Systems of Systems

Case Study 3: Nutrient Flows, Irrigation, and Desertification
Further Reading
Sample Problems
References

Chapter 4: Dynamic Systems

4.1 System State
4.2 Randomness
4.3 Analysis
4.3.1 Correlation
4.3.2 Stationarity
4.3.3 Transformations

Case Study 4: Water Levels of the Oceans and Great Lakes
Further Reading
Sample Problems
References

Chapter 5: Linear Systems

5.1 Linearity
5.2 Modes
5.3 System Coupling
5.4 Dynamics
5.5 Control of Dynamic Systems
5.6 Non-normal Systems

Case Study 5: System Decoupling
Further Reading
Sample Problems
References

Chapter 6: Nonlinear Dynamic Systems — Uncoupled

6.1 Simple Dynamics
6.2 Bifurcations
6.3 Hysteresis and Catastrophes
6.3.1 Catastrophic State Transition 6.3.2 System Irreversibility and Hysteresis
6.4 System Behaviour near Folds
6.5 Overview
Case Study 6: Climate and Hysteresis
Further Reading
Sample Problems
References

Chapter 7: Nonlinear Dynamic Systems — Coupled

7.1 Linearization
7.2 2D Nonlinear Systems
7.3 Limit Cycles and Bifurcations
7.4 Control and Stabilization
Case Study 7: Geysers, Earthquakes, and Limit Cycles
Further Reading
Sample Problems
References

Chapter 8: Spatial Systems

8.1 PDEs
8.2 PDEs and Earth Systems
8.3 Discretization
8.3.1 Discretization in Time
8.3.2 Discretization in Space
8.4 Spatial Continuous-State Models
8.5 Spatial Discrete-State Models
8.6 Agent Models
Case Study 8: Global Circulation Models
Further Reading
Sample Problems
References

Chapter 9: Power Laws and Non-Gaussian Systems

9.1 The Gaussian Distribution
9.2 The Exponential Distribution
9.3 Heavy Tailed Distributions
9.4 Sources of Power Laws
9.5 Synthesis and Analysis of Power Laws
Case Study 9: Power Laws in Social Systems
Further Reading
Sample Problems
References

Chapter 10: Complex Systems

10.1 Spatial Nonlinear Models
10.1.1 Phase Transitions
10.1.2 Criticality
10.2 Self-Organized Criticality
10.3 Emergence
10.4 Complex Systems of Systems
Case Study 10: Complex Systems in Nature
Further Reading
Sample Problems
References

Chapter 11: Observation and Inference

11.1 Forward Models
11.2 Remote Measurement
11.3 Resolution
11.3.1 Measurement Resolution
11.3.2 State Resolution
11.4 Inverse Problems
Case Study 11A: Sensing Synthetic Aperture Radar
Case Study 11B: Inversion Atmospheric Temperature
Further Reading
Sample Problems
References

Chapter 12: Water

12.1 Ocean Acidification
12.2 Ocean Garbage
12.3 Groundwater
Case Study 12: Satellite Remote Sensing of the Ocean
Further Reading
Sample Problems
References

Chapter 13: Concluding Thoughts

Further Reading
Sample Problems
References

Appendix A: Matrix Algebra

Further Reading
References

Appendix B: Random Variables and Statistics

Further Reading
References

Appendix C: Notation Overview

Further Reading
References



(Page last updated December 14, 2016, [an error occurred while processing this directive])