Reading List
From Complex Systems
Contents |
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Popular books
For better or worse, there are many popular books on complex systems. They promote the public awareness of the field, which is a good thing. They give the beginning research students an idea of its flavour, which is undoubtedly a good thing. At the same time, they tend to oversimplify things, conveying a false sense of mathematical tractability of the subject, which is not so good. The reader should appreciate the complexity of the subject (no puns intended), even though the exposition in some of these books may make it sounds simple. They are popular literature, after all.
- S. Wolfram. A New Kind of Science. Wolfram Media, 2002.
- P. Bak. How Nature Works: The Science of Self-organized Criticality. Springer-Verlag, 1999.
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Applications
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Economics and Sociology
- B. Skyrms. The Stag Hunt and the Evolution of Social Structure. Cambridge University Press, 2003.
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Finance
- Didier Sornette. Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press, 2004.
- Abstract
- The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of materials. In this book, Didier Sornette boldly applies his varied experience in these areas to propose a simple, general theory of how, why, and when stock markets crash.
- Any investor or investment professional who seeks a genuine understanding of looming financial disasters should read this book. Physicists, geologists, biologists, economists, and others will welcome Why Stock Markets Crash as a highly original study of the exciting and sometimes fearsome — but no longer quite so unfathomable — world of stock markets.
- Benoit B. Mandelbrot. The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward. Profile Books, 2005.
- Abstract
- With the invention of fractal geometry, mathematical superstar Benoit Mandelbrot forever changed the way we understand the mysteries of nature and influenced a host of modern fields, from chaos theory to computer animation. Now, together with science journalist and former Wall Street Journal editor Richard L. Hudson, Mandelbrot turns a fractal eye to the behavior of financial markets and overturns the "random walk" theory that is the underpinning of all contemporary financial analysis. Markets, we learn, are far riskier than we have wanted to believe.
- The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With his fractal models, the (mis)behavior of the world's markets — from the gyrations of IBM's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate — can be understood in more accurate terms than the tired theories of yesteryear.
- For the past forty years, Mandelbrot has been studying the underlying mathematics of finance — and this book relates his personal voyage of discovery. From his father's wartime garment business, his research on the American cotton market, and his studies of the Nile River's floods, Mandelbrot draws many unusual insights — the insights of a maverick scientist. He has proven that many of the fundamental assumptions of financial theory are wrong, and in the past decade a growing number of financiers and economists have started listening. The models he has built faithfully replicate real-world price series, illustrate the manner in which market turbulence clusters, and show that no investment horizon is inherently better than another — volatility "scales" the same over hours or decades. Financial markets do not fluctuate according to a "random walk" mode; they operate with their own sense of "market time" that does not correspond to hours and minutes as the wall clock counts them.
- The (Mis)behaviour of Markets is a revolutionary revelation of the standard tools and models of modern financial theory. Mandelbrot's fresh insights explode the false assumptions that have caused millions of investors, traders, and managers to underestimate the real risk of the market. His genius ensures that investors will never see the market — or their portfolios — the same way again.
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Biology
- R. Sole, B. C. Goodwin. Signs of Life: How Complexity Pervades Biology. Basic Books, 2002.
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Textbooks
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Information Theory
- M. Li, P. Vitanyi. An Introduction to Kolmogorov Complexity and Its Applications. Graduate Texts in Computer Science. 2nd Edition. Springer.
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Complex Systems
- Y. Bar-Yam. Dynamics of Complex Systems (Studies in Nonlinearity). Westview Press, 2003.
- G. Flake. The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems and Adaptation. The MIT Press, 2000.
- D. Sornette. Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools. 2nd Edition. Springer-Verlag, 2006.
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Statistical Mechanics
- H. J. Jensen. Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems. Cambridge University Press, 1998.
- K. Christensen, N. R. Moloney. Complexity and Criticality. Imperial College Press, 2005.
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Complex Networks
- Fan Chung, Linyuan Lu. Complex Graphs and Networks. Regional Conference Series in Mathematics. Published for the Conference Board for Mathematical Sciences (CBMS) by the American Mathematical Society (Providence, Rhode Island) with support from the National Science Foundation, 2006.
- Abstract
- Through examples of large complex graphs in realistic networks, research in graph theory has been forging ahead into exciting new directions. Graph theory has emerged as a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or, more generally, any graph representing relations in massive data sets.
- How will we explain from first principles the universal and ubiquitous coherence in the structure of these realistic but complex networks? In order to analyze these large sparse graphs, we use combinatorial, probabilistic, and spectral methods, as well as new and improved tools to analyze these networks. The examples of these networks have led us to focus on new, general, and powerful ways to look at graph theory. The book, based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, presents new perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate this information age.
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Dynamical Systems and Chaos
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Theory
- R. L. Devaney. A First Course in Chaotic Dynamical Systems: Theory and Experiment (Studies in Nonlinearity). Perseus Books, 1999.
- R. L. Devaney (Editor). Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets (Proceedings of Symposia in Applied Mathematics). American Mathematical Society, 1995.
- R. L. Devaney. An Introduction to Chaotic Dynamical Systems (Studies in Nonlinearity). Westview Press, 2003.
- M. W. Hirsch. Differential Equations, Dynamical Systems & An Introduction to Chaos. Second Edition. Elsevier Academic Press.
- Abstract: This best-selling, classic text by eminent mathematicians Hirsch and Smale has captured the beauty and relative accessibility of chaotic phenomena for three decades. This field has motivated scientists and engineers in many disciplines to understand how differential equations and dynamical systems phenomena appear in virtually every area of science: chemistry, electrical engineering, celestial mechanics, ecological systems, and beyond. Hirsch, Smale, and Devaney's second edition reflects changes in research and teaching, including: simplified treatment of linear algebra; many new and updated applications; several chapters that discuss discrete dynamical systems; simplification of many theorem hypotheses; new detailed discussion of chaotic behaviour in the Lorenz attractor and Shil'nikov system, and the double scroll attractor.
- Oded Galor. Discrete Dynamical Systems. Springer-Verlag Berlin Heidelberg, 2007.
- Abstract:
- This book provides an introduction to discrete dynamical systems — a framework of analysis that is commonly used in the fields of biology, demography, ecology, economics, engineering, finance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, first-order, linear, autonomous systems. The fundamental insights about the forces that affect the evolution of these elementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non-autonomous dynamical systems are established.
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Practice: Implementing the Models
- R. L. Devaney. Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics. Addison Wesley, 1980.
- W.-H. Steeb. The Nonlinear Workbook. 3rd Edition. World Scientific, 2005.
- S. J. Lynch. Dynamical Systems with Applications using MATLAB. Birkhauser Boston, 2004.
- S. J. Lynch. Dynamical Systems with Applications using Maple. Birkhauser Verlag AG, 2000.
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Multi-Agent Systems
- M. J. Wooldridge. An Introduction to Multi-agent Systems. John Wiley and Sons, 2002.
- G. Weiss. Multiagent Systems: A Modern Approach to Distributed Artificial Intelligence. The MIT Press, 2000.
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Online Resources
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To be read
I haven't read the following books, but I'm going to read them soon.
- M. Batty. Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals. The MIT Press, 2005.
- F. Vega-Redondo. Complex Social Networks. Econometric Society Monographs. Cambridge University Press.
