Introduction to Complex Systems

Paul Fieguth is a professor in Systems Design Engineering at the University of Waterloo in Ontario, Canada. He has longstanding research interests in statistical signal and image processing, hierarchical algorithms, machine learning, and the interdisciplinary applications of such methods, particularly to problems in medical imaging, remote sensing, and scientific imaging. With Springer he has published two successful books: Statistical Image Processing and Multidimensional Modeling (2011) and An Introduction to Complex Systems (2017, 1st edition).

• 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 Systems of Complex 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 11A: Sensing— Synthetic Aperture Radar.- Case Study 11B: 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 Pandemics and Complex Systems.-  13.1 Pandemic Dynamics.- 13.2 Pandemic Models.- 13.3 Pandemic Anticipation.- Case Study 13: Pandemic Inverse Problems and Inference.- Further Reading.- Sample Problems (Partial Solutions in Appendix E).- 14 Concluding Thoughts.- Further Reading.- Part I Appendices.- A Matrix Algebra.- B Random Variables andStatistics.- C System Decoupling.- D Notation Overview.- E End of Chapter Solutions.- Index.