Introduction to Complex Systems
2006 Winter

Topic: The discipline of 'Complex Systems' studies how collective behavior emerges due to interaction of the parts of a system. You will learn the basic concepts and methods of complex system research. Both historical and present-day approaches will be mentioned. It will be emphasized that since many systems of very different fields, such as physics, chemistry, biology, economics, psychology and sociology etc. have similar architecture, very different phenomena of nature and society can be analyzed and understood by using a common approach called 'systems thinking'.

Goal: The first goal is to teach WHY complex systems research is important in understanding the structure, function and dynamics of complex natural and social phenomena. The second goal is to give an introductory overview about HOW the fundamental methods of complex systems research works. The course is not highly technical mathematically, but teaches and uses the basic mathematical notions of dynamical system theory. Not only students of science majors, but social science students (with some mathematical interest and skill) are expected to take the class.

Course Structure: Ten topics will be discussed. We shall spend one week on each topic.

Group tasks will be assigned. Reports on group tasks are due on tens week M and W.

Exam: There will be a one hour long midterm written and final examination.

Grades are calculated by your results in mid-term (25%), group tasks (25%) and final exams (50%).

Extra-class activities in connection with complex systems research (e.g. Writing of simulation programs, participation in class discussion, active participation in the events organized by the Center for Complex Systems Studies) will also be considered in assigning your final grade.

Reading: Specific readings will be assigned individually. Reports about the paper is required.

Simulations: Simulations with Netlogo will be required. NetLogo is a cross-platform multi-agent programmable modeling environment

Special event: February 20th Monday: the class is rescheduled for a LAC event: Dow 226, 8:00 p.m. Santiago Schnell, Professor with the Biocomplexity Institute at Indiana University, Bloomington, will speak on "Systems Biology and Complex Systems". The participations is obligatory.

• What are the characteristics of simple and complex systems?
• Structural, functional, dynamic and algorithmic complexity.
• Complexity in physics, biology, economics, and sociology.

• http://en.wikipedia.org/wiki/Complex_system
• Complex Systems: The Intellectual Landscape (This is the preliminary draft of the first chapter of the book 'Complexity Expained' I am writing now for the Springer Publishing Company.
Positive and Negative Feedback in Politics Frank R. Baumgartner and Bryan D. Jones to be downloaded from http://polisci.la.psu.edu/faculty/Baumgartner/contents.htm

• Reductionist success stories versus the importance of the organization principles. Capsule history of atomic phyisics and molecular biology
• Some fundamental theories of the 20th centuries are reviewed: System theory, Cybernetics. Theory of Dissipative Structures, Synergetics and Catastrophe Theory.

• http://en.wikipedia.org/wiki/Systems_theory
• http://en.wikipedia.org/wiki/Complexity

• Ancient and modern time concepts.
• From Kepler to Newton: The dynamic world view.
• States and processes: beyond Mechanics.
• Direction of evolution.
• The Lotka-Volterra model: roots in chemistry and population dynamics. General framework of systems with competitive and cooperative interactions.

• Chaos and fractals proved to be very efficient mathematical concepts to understand temporal and spatial complexity.
• Elementary mathematical explanation.
• Chaos in chemistry, population dynamics, brain and economics.
• Fractals in physiology.
• The fractal nature of organizations.

• http://en.wikipedia.org/wiki/Chaos_theory
• http://en.wikipedia.org/wiki/Fractal
• http://ccl.northwestern.edu/netlogo/models/KochCurve
• http://ccl.northwestern.edu/netlogo/models/SierpinskiSimple

Self-organization is a vague concept in many respects, still a powerful notion of modern science. Specifically and counter-intuitively, noise proved to have beneficial (sometiems indispensable) role in constructing macroscopically ordered structures. Elementary mathematical models of noise-induced ordering. Synchronized activity in a population may emerge without external command (e.g. flashing of fireflies)

In physics, a critical point is a point at which a system radically changes its behavior or structure, for instance, from solid to liquid. In standard critical phenomena, there is a control parameter which an experimenter can vary to obtain this radical change in behavior. In the case of melting, the control parameter is temperature. Self-organized critical phenomena, by contrast, is exhibited by driven systems which reach a critical state by their intrinsic dynamics, independently of the value of any control parameter. The archetype of a self-organized critical system is a sand pile. Sand is slowly dropped onto a surface, forming a pile. As the pile grows, avalanches occur which carry sand from the top to the bottom of the pile. At least in model systems, the slope of the pile becomes independent of the rate at which the system is driven by dropping sand. Self-organized criticality is a useful concept and was used to explain statistical features for a wide variety of open systems with many components, ranging from geology to biology and economics. A few illustrative examples will be given.

The Schelling segregation model. Thomas Schelling, in 1971, showed that a small preference for one's neighbors to be of the same color could lead to total segregation. (He has been awarded by the Nobel prize in economcs in 2005).

• Philip Ball: Utopia theory
• http://ccl.northwestern.edu/netlogo/models/Fireflies
• http://www.timharford.com/favourites/schelling.htm

• http://ccl.northwestern.edu/netlogo/models/Segregation

Game theory emerged as an important tool for treating the problem of necessary cooperation to avoid (nuclear and other) catastrophes. The most famous game is the Prisoner's Dilemma. The fundamental types of games will be discussed. Illustrative examples of applications for evolutionary theory and economics will be given.

• The Tragedy of the Commons: Garrett Hardin, Science, 162(1968):1243-1248.
• http://en.wikipedia.org/wiki/Tragedy_of_the_commons
• http://levine.sscnet.ucla.edu/general/whatis.htm
• Steven J. Brams: Game theory and the Cuban missile crisis

Real world systems in many cases can be represented by networks. Networks can be seen everywhere (neural networks of the brain, food webs and ecosystems, electric power networks, system of social connections, global financial network, the world-wide web). Since the famous social psychological experiment of Stanley Milgram, it is known that from a certain point of view we live in a 'small world.' However, the relationships between the structure of large networks and their dynamical properties generally are not well known. The performance of many biological, ecological, economical, sociological, communication and other networks can be illuminated by using new approaches coming from graph theory, statistical physics and nonlinear dynamics. Examples will be given to illustrate the power of the new approaches in the understanding of the organization of social structures. Specifically, scientific collaboration networks will be analyzed.

• Péter Érdi: Complex (not only neural) network
• Hayes B: Graph Theory in Practice: Part I, American Scientist 88(1) 2000
• Hayes B: Graph Theory in Practice: Part II, American Scientist 88(2) 2000
• http://ccl.northwestern.edu/netlogo/models/SmallWorlds
• http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment
• A more advanced reading: Newman, MEJ: The structure and function of complex networks

Though molecular biology was very successful to understand the moleular basis of heritability, now the integration of different levels from molecular and cellular to system level seems to be necessary to undertsand normal and pathological biological functions, for discivering new therapeutic strategies. Medical sciences and pharmacology should benefit from adopting the system levels's perspective.

• Kitano, H. (2002) Systems biology: a brief overview, Science, March, 1; 295(5560):1662-4.
• Eduard Kellenberger: The evolution of molecular biology. EMBO reports 5: 546-549. (June 2004)
• Regenmortel MH van: Reductionism and complexity in molecular biology: scientists now have the tools to unravel biological complexity and overcome the limitations of reductionism. EMBO Reports 5: 1016-1020. 2004

Simple models can illuminate essential dynamics of complex, and crucially important social systems. Models of war and arm races can be constructed within the framework of the Volterra-Lotka model

• http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology
• http://ccl.northwestern.edu/netlogo/models/RumorMill