Complex Systems Science


Complex Systems Science is an umbrella term for a range of concepts and approaches to deal with systems that are more than just complicated. Complicated systems are essentially just scaled up versions of more simple systems, that can be analysed by separating the system into its component parts and understanding how those parts behave. Complex systems are systems in which the interactions and dynamic, changing, connections between component parts lead to the emergence of behaviours and entities which are not found at the level of the component parts.

Unfortunately ‘complexity’ and ‘chaos’ have been at times over-hyped and even used to smuggle in woolly thinking under the cover of technical-sounding terms and phrases, accompanied by much arm-waving – particularly in business and leadership training. As a result, plenty of people have mistakenly concluded that ‘complex systems science’ is an empty box. Not so. Complex systems science is an inter-disciplinary field with a firm grounding in the ‘hard’ physical sciences of physics, chemistry and biology, with extensive applications and further developments in the social sciences. There’s much to be learned from complex systems science. Here are a few resources and links that might help.

Papers & Chapters


Alligood, K.T., Sauer, T.D. and Yorke, J.A., (1996) Chaos: An Introduction to Dynamical Systems, Springer, New York, Berlin & Heidelberg, xvii + 603 pp.

Auyang, S.Y., (1998) Foundations of Complex System Theories: In Economics, Evolutionary Biology and Statistical Physics, Cambridge University Press, Cambridge, New York, Melbourne & Madrid, xii + 404 pp. [One of the best books on complex systems I have ever come across]

Axelrod, R., (2006) The Evolution of Cooperation, Revised Edition; Basic Books, New York,

Batty, M., (2005) Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals, MIT Press, Cambridge, MA & London, xxiii + 565 pp.

Bhaskar, R., Esbjörn-Hargens, S., Hedlund, N. and Hartwig, M. (Eds.), (2016) Metatheory for the Twenty-First Century: Critical Realism and Integral Theory in Dialogue, Routledge, London, xxxii + 325 pp.

Boccara, N., (2010) Modeling Complex Systems, Second Edition; Graduate Texts in Contemporary Physics; Springer Science+Business Media, New York, Dordrecht, Heidelberg & London, xvii + 489 pp.

Davis, M. (Ed.) (2004) The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, Originally published in 1965 by Raven Press Books; Dover, Mineola, NY, 413 pp.

Dörner, D., (1996) The Logic of Failure: Recognizing and Avoiding Error in Complex Situations, trans. Kimber, R. and Kimber, R.; Originally published in German as Die Logik des Misslingens, 1989; Basic Books, New York, 222 pp.

Epstein, J.M. and Axtell, R., (1996) Growing Artificial Societies: Social Sciences from the Bottom Up, MIT Press, Cambridge, MA, xv + 208 pp.

Epstein, J.M., (2006) Generative Social Science: Studies in Agent-Based Computational Modeling, Princeton University Press, Princeton, NJ, xx + 356 pp.

Garey, M.R. and Johnson, D.S., (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman & Co., New York, x + 338 pp.

Geyer, R. and Rihani, S., (2008) Complexity and Public Policy: A New Approach to 21st Century Politics, Policy and Society, Routledge, London, 224 pp.

Gilbert, N. and Troitzsch, K.G., (2005) Simulation for the Social Scientist, 2nd Edition; Open University Press, Maidenhead & New York, xi+295 pp.

Gimblett, H.R. (Ed.) (2002) Integrating Geographic Information Systems and Agent-Based Modeling Techniques for Simulating Social and Ecological Processes, Studies in the Sciences of Complexity; Oxford University Press for the Santa Fe Institute, Oxford & New York, xiv + 327 pp.

Gleick, J., (2008) Chaos: Making a New Science, 20th Anniversary Edition; Penguin, London, 384 pp.

Gros, C., (2008) Complex and Adaptive Dynamical Systems: A Primer, Springer Complexity; Springer-Verlag, Berlin & Heidelberg, xiv + 262 pp.

Johnson, N., (2009) Simply Complexity: A Clear Guide to Complexity Theory, Oneworld Publications, 256 pp.

Kauffman, S., (1995) At Home in the Universe: The Search for Laws of Complexity, Penguin, London, 321 pp.

Kiel, L.D. and Elliott, E. (Eds.), (1996) Chaos Theory in the Social Sciences: Foundations and Applications, University of Michigan Press, Ann Arbor, viii + 349 pp.

Medio, A., (1992) Chaotic Dynamics: Theory and Applications to Economics, Cambridge University Press, Cambridge, xv + 344 pp.

Medio, A. and Lines, M., (2001) Nonlinear Dynamics: A Primer, Cambridge University Press, Cambridge & New York, xiii + 300 pp.

Miller, J.H. and Page, S.E., (2007) Complex Adaptive Systems: An Introduction to Computational Models of Social Life, Princeton University Press, Princeton, NJ, 284 pp.

Mitchell, M., (2009) Complexity: A Guided Tour, Oxford University Press, Oxford, xvi + 349 pp.

Mitchell, S.D., (2009) Unsimple Truths: Science, Complexity and Policy, University of Chicago Press, Chicago & London, x + 149 pp.

Norberg, J. and Cumming, G.S. (Eds.), (2008) Complexity Theory for a Sustainable Future, Colombia University Press, New York, xv + 315 pp.

Page, S.E., (2011) Diversity and Complexity, Primers in Complex Systems; Princeton University Press, Princeton NJ & Oxford, x + 291 pp.

Room, G., (2011) Complexity, Institutions and Public Policy: Agile Decision-Making in a Turbulent World, Edward Elgar, Cheltenham UK & Northampton MA, viii + 383 pp.

Scheffer, M., (2009) Critical Transitions in Nature and Society, Princeton Studies in Complexity; Princeton University Press, Princeton NJ, xi + 384 pp.

Steeb, W.-H., (2011) The Nonlinear Workbook: Chaos, Fractals, Cellular Automata, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic with C++, Java and SymbolicC++ Programs, 5th Edition; World Scientific, Singapore, 644 pp.

Strogatz, S.H., (1994) Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press, Cambridge, MA, xi + 497 pp.

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Papers & Chapters

Arthur, W.B., (1993) “Why Do Things Become More Complex?” Scientific American, Vol. 268, No. 5, May, p. 92.

Arthur, W.B., (1999) “Complexity and the Economy“, Science, Vol. 284, No. 5411, 2 April, pp. 107-109.

Crutchfield, J.P., Farmer, J.D., Packard, N.H. and Shaw, R.S., (1986) “Chaos”, Scientific American, Vol. 255, No. 6, December, pp. 38-49.

Cucker, F. and Smale, S., (2007) “On the Mathematics of Emergence”, Japanese Journal of Mathematics, Vol. 2, No. 1, March, pp. 197-227.

Egolf, D.A., (2000) “Equilibrium Regained: From Nonequilibrium Chaos to Statistical Mechanics”, Science, Vol. 287, No. 5450, 7 January, pp. 101-104.

Ford, J., (1983) “How Random is a Coin Toss?” Physics Today, April, pp. 40-47.

Foster, J., (2005) “From Simplistic to Complex Systems in Economics”, Cambridge Journal of Economics, Vol. 29, No. 6, November, pp. 873-892.

Holt, R.P.F., Rosser, J.B. and Colander, D., (2011) “The Complexity Era in Economics”, Review of Political Economy, Vol. 23, No. 3, pp. 357-369.

Lebowitz, J.L. and Penrose, O., (1973) “Modern Ergodic Theory”, Physics Today, Vol. 26, No. 2, February, pp. 23-29.

Licata, I., (2010) “Almost-Anywhere Theories: Reductionism and Universality of Emergence”, Complexity, Vol. 15, No. 6, July – August, pp. 11-19.

Manson, S.M., (2008) “Does Scale Exist? An Epistemological Scale Continuum for Complex Human-Environment Systems”, Geoforum, Vol. 39, No. 2, March, pp. 776-788.

Metcalfe, J.S., (2010) “Complexity and Emergence in Economics: The Road from Smith to Hayek (via Marshall and Schumpeter)”, History of Economic Ideas, Vol. 18, No. 2, pp. 45-76.

Pepper, S.C., (1926) “Emergence”, Journal of Philosophy, Vol. 23, No. 9, pp. 241-245.

Rosser, J.B., Jr., (1999) “On the Complexities of Complex Economic Dynamics”, Journal of Economic Perspectives, Vol. 13, No. 4, Fall, pp. 169-192.

Rosser, J.B., Jr., (2010) “Is a Transdisciplinary Perspective on Economic Complexity Possible?” Journal of Economic Behavior & Organization, Vol. 75, No. 1, July, pp. 3-11.

Saari, D.G., (1995) “Mathematical Complexity of Simple Economics“, Notices of the American Mathematical Society, Vol. 42, No. 2, February, pp. 222-230.

Underdal, A., (2010) “Complexity and Challenges of Long-Term Environmental Governance”, Global Environmental Change, Vol. 20, No. 3, August, pp. 386-393.

Wilson, K.G., (1979) “Problems in Physics with Many Scales of Length”, Scientific American, Vol. 241, No. 2, August, pp. 140-157.

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On the difference between simple and simplistic
“I would not give a fig for the simplicity this side of complexity, but I would give my life for the simplicity on the other side of complexity.”
U.S. Supreme Court Justice, Oliver Wendell Holmes Jr. – Source Unknown.

Sometimes ‘simple’ is just ‘silly’
“Indeed, ‘simplicity’ is quite a complicated notion and I confess to considerable impatience when silly models are defended by virtue of their simplicity …”
Economist Frank Hahn, one of the architects of general equilibrium theory, in Hahn, F.H., (1994) “An Intellectual Retrospect”, Banca Nazionale del Lavoro Quarterly Review, Vol. 47, No. 190, September, pp. 245-258; p. 251.

More is different
“An n-body problem for n = 1010 cannot be solved by extrapolating concepts and methods suitable to n = 2, not if the bodies interact.”
Auyang, S.Y., (1998) Foundations of Complex System Theories: In Economics, Evolutionary Biology and Statistical Physics, Cambridge University Press, Cambridge, New York, Melbourne & Madrid, xii + 404 pp; p. 115.

Large complex systems are not simply scaled up versions of small, simple systems, which can be treated with the same tools.
“This assumption, encapsulated in the slogan “The whole is nothing but the sum of the parts,” is correct if the parts do not interact, but unrelated constituents make trivial systems. Interaction and relation among the constituents make the whole more than the sum of the parts so that a larger whole is not merely a larger sum. They form structures, generate varieties, produce complexity, and make composition important. Microreductionism thinks that interactive effects can be accounted for by the addition of “and relations” in its slogan. Without pausing to consider how relations are summed, the breezy addition is a self-deception that blinds it to the efforts of many sciences, including the largest branch of physics. The theoretical treatment of structure formation in large composite systems with interacting constituents is tremendously difficult. It introduces a whole new ball game in science. Systems with a few million interacting constituents are not magnified versions of systems with a few constituents. … We can adequately describe the solar system in terms of individual planetary motions, but we cannot comprehend a galaxy with billions of stars solely in terms of individual stellar motions To understand galaxies we need new theoretical apparatus, including galactic notions such as spiral arms.”
Auyang, S.Y., (1998) Foundations of Complex System Theories: In Economics, Evolutionary Biology and Statistical Physics, Cambridge University Press, Cambridge, New York, Melbourne & Madrid, xii + 404 pp; pp. 4-5.

Why economic modelling is inherently more complex than modelling in other disciplines
“I want to emphasise strongly the point about economics being a moral science. … it deals with motives, expectations, psychological uncertainties. One has to be constantly on guard against treating the material as constant and homogeneous. It is as though the fall of an apple to the ground depended on the apple’s motives, on whether it is worth while falling to the ground, and whether the ground wanted the apple to fall, and on mistaken calculations on the part of the apple as to how far it was from the centre of the earth.”
John Maynard Keynes in a letter to Roy Harrod on 16 July 1938 in Keynes, J.M., (1971-89) The Collected Writings of John Maynard Keynes, Macmillan & St Martin’s Press for the Royal Economic Society, London & New York, Vol. XIV, p. 300.

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Center for Social Complexity – George Mason University

Complex Systems Research Centre – Cranfield University School of Management

The ARC Centre for Complex Systems

Complexity Digest – A news digest of publications & events related to complex systems science.

New England Complex Systems Institute – “A non-profit research and education institute developing new scientific methods, and applying them to the challenges of society.” Based in Cambridge, Massachusetts.

Resilience Alliance – “A multidisciplinary research group that explores the dynamics of complex adaptive systems.”

Santa Fe Institute – One of the mother ships of complex systems research.

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Last updated: 7 July 2017