An Introduction to Complex Systems

Paul Fieguth

List of Examples (see also Table of Contents)

The book contains a large number of examples, interspersed throughout the text, with an introductory and then more thoroughly developed case study at the beginning and end of every chapter, with the end of chapter studies designed to illustrate and apply the concepts of the chapter to a problem of practical interest:

Case Study 2: Global Warming and Climate Change
Case Study 3: Nutrient Flows, Irrigation, and Desertification
Case Study 4: Water Levels of the Oceans and Great Lakes
Case Study 5: System Decoupling
Case Study 6: Climate and Hysteresis
Case Study 7: Geysers, Earthquakes, and Limit Cycles
Case Study 8: Global Circulation Models
Case Study 9: Power Laws in Social Systems
Case Study 10: Complex Systems in Nature
Case Study 11A: Sensing — Synthetic Aperture Radar
Case Study 11B: Inversion — Atmospheric Temperature
Case Study 12: Satellite Remote Sensing of the Ocean
Application 11: Multi-Instrument Fusion of Porous Media

The goal of the text is to take concepts of nonlinear dynamics, complex systems, power-law distributions, and system sensing beyond their mathematical definition, and to try to develop some degree of insight and intuition. The large number of examples in the text are designed as asides, to numerically explore individual topics. As a sample, links are provided to two examples:

Example 3.1: Three systems and their envelopes
Example 3.2: Complete Accounting
Example 3.3: Entropy Reduction
Example 3.4: Society, Civilization, and Complexity
Example 3.5: Energy Returned on Energy Invested (EROEI)
Example 3.6: Maximum Power Principle
Example 3.7: Global Flows I

Example 4.1: System Examples
Example 4.2: Correlation Lag Mechanical System
Example 4.3: Correlation Lag Thermal System

Example 5.1: The Exponential Function
Example 5.2: Coupled Systems
Example 5.3: Resilience I Linear Systems

Example 6.1: Population Growth
Example 6.2: Bead on a Hoop
Example 6.3: System Perturbations
Example 6.4: Deliberate Hystereses
Example 6.5: Playing with Blocks
Example 6.6: Hysteresis in Freshwater Lakes

Example 7.1: Nonlinear Competing Dynamics
Example 7.2: Basins for Root Finding
Example 7.3: Resilience II Nonlinear Systems
Example 7.4: Creating and Finding a Limit Cycle
Example 7.5: An Alarm Bell as Limit Cycle
Example 7.6: Limit Cycles in Economics
Example 7.7: The Tragedy of the Commons
Example 7.8: Societal Dynamics

Example 8.1: Spatial Discretization
Example 8.2: The Spatial Dynamics of Human Impact
Example 8.3: Two-Box Lumped-Parameter Model
Example 8.4: Global Flows II
Example 8.5: Spatial Nonlinear Systems and Traffic Jams

Example 9.1: Memory and Exponentials
Example 9.2: Power Laws in Finance
Example 9.3: Power Laws in Weather
Example 9.4: Power Laws and Fraud Statistics
Example 9.5: Power Laws and Cities
Example 9.6: Power Laws and Discount Functions

Example 10.1: Ferromagnetic Phase Change
Example 10.2: Spatial SOC Earthquakes
Example 10.3: Slime Mould Emergence
Example 10.4: Resilience III Complex Systems

Example 11.1: Indirect Inference
Example 11.2: Can a Space Telescope Read a Newspaper?
Example 11.3: Measurements and Constraints

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