An introduction to complex systems : society, ecology, and nonlinear dynamics / Paul Fieguth.

Format:

Book

Author/Creator:

Fieguth, Paul, author.

Language:

English

Subjects (All):

Nonlinear mechanics.

Genre:

Electronic books.

Physical Description:

1 online resource : illustrations (chiefly color)

Edition:

Second edition.

Place of Publication:

Cham : Springer, [2021]

System Details:

text file

Summary:

Complex Systems lie at the heart of a variety of large-scale phenomena of great significance - global warming, ice ages, water, poverty, pandemics - and this text uses these case studies as motivations and contexts to explore complex systems and related topics of nonlinear dynamics and power-law statistics. Although detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or perspective. Instead, the book seeks to emphasize understanding, concepts, and ideas, in a way that is mathematically rigorous, so that the concepts do not feel vague, but not so technical that the mathematics get in the way. The book is intended for students in technical domains such as engineering, computer science, physics, mathematics, and environmental studies. This second edition adds nine new examples, over 30 additional problems, 50 additional figures, and three new chapters offering a detailed study of system decoupling, extensive solutions to chapter problems, and a timely discussion on the complex systems challenges associated with COVID-19 and pandemics in general.

Contents:

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

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

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

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

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

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

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

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

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

12 Water

12.1 Ocean Acidification

12.2 Ocean Garbage

12.3 Groundwater

Case Study 12: Satellite Remote Sensing of the Ocean

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

Sample Problems (Partial Solutions in Appendix E)

14 Concluding Thoughts

Part I Appendices

A Matrix Algebra

B Random Variables and Statistics

C System Decoupling

D Notation Overview

E End of Chapter Solutions

Index.

Notes:

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed September 14, 2021).

ISBN:

9783030631680

3030631680

OCLC:

1267337470

Access Restriction:

Restricted for use by site license.