An Introduction to Complex Systems: Society, Ecology, and Nonlinear Dynamics

by Paul Fieguth

1 Introduction.- 2 Global Warming and Climate Change.- Further Reading.- 3 Systems Theory.- 3.1 Systems & Boundaries.- 3.2 Systems & Thermodynamics.- 3.3 Systems of Systems.- Case Study 3: Nutrient Flows, Irrigation, and Desertification.- Further Reading.- Sample Problems.- 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.- 5 Linear Systems.- 5.1 Linearity.- 5.2 Modes.- 5.3 System Coupling.- 5.4 Dynamics.- 5.5 Non-Normal Systems.- Case Study 5: System Decoupling.- Further Reading.- Sample Problems.- 6 Nonlinear Dynamic Systems - Uncoupled.- 6.1 Simple Dynamics.- 6.2 Bifurcations.- 6.3 Hysteresis and Catastrophes.- 6.4 System Behaviour near Folds.- 6.5 Overview.- Case Study 6: Climate and Hysteresis.- Further Reading.- Sample Problems.- 7 Nonlinear Dynamic Systems - Coupled.- 7.1 Linearization.- 7.2 2D Nonlinear Systems.- 7.3 Limit Cycles and Bifurcations.- Case Study 7: Geysers, Earthquakes, and Limit Cycles.- Further Reading.- Sample Problems.- 8 Spatial Systems.- 8.1 PDEs.- 8.2 PDEs & Earth Systems.- 8.3 Discretization.- 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.- 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.- 10 Complex Systems.- 10.1 Spatial Nonlinear Models.- 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.- 11 Observation & Inference.- 11.1 Forward Models.- 11.2 Remote Measurement.- 11.3 Resolution.-11.4 Inverse Problems.- Case Study 11 Sensing- Synthetic Aperture Radar.- Case Study 11 Inversion- Atmospheric Temperature.- Further Reading.- Sample Problems.- 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.- 13 Concluding Thoughts.- Further Reading.- Part I Appendices.- Index.

Genres: Biology

360 pages, Paperback

Published December 6, 2016

Reviews

[Lorien · Rating 5 out of 5]

For a student who is reading the text to accompany Professor Fieguth's course, this is a five-star experience. It serves up an elegant introduction into the applied science of complexity, specifically with respect to complex societal and ecological problems.

The mathematical theory requires an undergraduate-level understanding of linear algebra to decipher, but this is appropriate for the audience of the text. For those who may be bogged down by the math, Prof. Fieguth gives ample examples, case studies, and suggestions for further reading that would be enough to allow a reader with no post-secondary education to grasp the big ideas.

It's beautiful, it's elegant, and the ideas are filling a void that I didn't know I had in my SYDE education. We've gotten a bit of systems theory in our design courses, but no course and text has so directly given us the theory and immediately applied it with the technical rigor we would expect of an engineering elective. If you're a systems student whose academic palate is remotely intrigued by flavours such as climate dynamics, urban sprawl, remote sensing, or ecological nutrient flow, accept this as your holy text for one winter term and you won't regret it.

Professor Fieguth, thank you for your work on the course, on the text, and in the SYDE department!