Introduction to Complex Systems

2008 Winter

OU313A M-W-F- 11:50a 1:05p

Instructor: Péter Érdi, Henry R. Luce Professor of Complex Systems Studies

Office: OU 208/B. email: perdi@kzoo.edu

TA: Dr. Gábor Borgulya

Topics: 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 tenth 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%).

Readings: My book 'Complexity Explained' (CE) was published recently. The book is not a formal textbook, it should be read as an intellectual background. Don't worry (very much): the minimal necessary math will be explained.

Computational Tools

Computer simulations with Netlogo will be required.

NetLogo is a cross-platform multi-agent programmable modeling environment:

http://ccl.northwestern.edu/netlogo/ .

1. COMPLEX SYSTEMS: CONCEPTUAL INTRODUCTION

Topics:

The century of complexity?

Structural, functional, dynamic and algorithmic complexity

Characteristics of simple systems

Characteristic of complex systems [circular causality, feedback loops, logical paradoxes; butterfly effects and unpredictability].

Readings:

CE Chapter 1

http://en.wikipedia.org/wiki/Complex_system

2. HISTORY OF COMPLEX SYSTEM RESEARCH

Topics:

Reductionist success stories versus the importance of the organization principles. Capsule history of atomic physics and molecular biology

Some fundamental theories of the 20th centuries are reviewed:

System theory, Cybernetics

Theory of Dissipative Structures, Synergetics and Catastrophe Theory

Multistability: a general concept.

Readings: CE Chapter 2

3. FROM CLOCK WORK WORLD VIEW to IRREVERSIBILITY

Topics:

Ancient and modern time concepts

The mechanical clock

From Kepler to Newton: The dynamic world view. States and processes: Mechanics versus Thermodynamics

Models of oscillation:

The Lotka-Volterra model: roots in chemistry and population dynamics. General framework of systems with competitive and cooperative interactions. Limit cycles. Direction of evolution. Cyclic Universe?

Readings: CE Chapter 3.

4. CHAOS and FRACTALS in NATURE and SOCIETY

Topics:

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. Complexity and art.

Readings:

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

CE 7.2.3.

5. THE DYNAMIC WORLD VIEW IN ACTION

Topics:

- From physical states to general states.

- Dynamic laws

- How animals with flashy coats get their patterns?

- Connectivity, stability and diversity in ecology

- The propagation of biological and social epidemics

- Dynamic models of war and love

- Segregation dynamics (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 economics in 2005.)

- Opinion dynamics

Readings:

http://www.bioedonline.org/news/news.cfm?art=2705

CE 4.4. 4.5, 4.6.

NETLOGO simulations

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

6. GAME THEORY, EVOLUTION, POLITICAL SCIENCE

Topics:

Game theory emerged as an important tool for treating the problem of necessary cooperation to avoid (nuclear and other) catastrophes. The fundamental types of games will be discussed.

-The problem of fair division

-Prisoner's Dilemma

-Evolutionary game theory: evolution of cooperation

and of social norms

Readings:

CE 9.2

http://plato.stanford.edu/entries/game-theory/

http://levine.sscnet.ucla.edu/general/whatis.htm

The Tragedy of the Commons: Garrett Hardin (1968) Science

http://dieoff.org/page95.htm

http://en.wikipedia.org/wiki/Tragedy_of_the_commons

http://levine.sscnet.ucla.edu/general/whatis.htm

http://en.wikipedia.org/wiki/Evolutionary_stable_strategy

Steven J. Brams:

Game theory and the Cuban missile crisis

http://plus.mathsorg/issue13/features/brams/

7. STATISTICAL LAWS: FROM SYMMETRIC TO ASSYMETRIC

Topics:

Generally (continuous) biological variables (from heights, and weights to IQ) are characterized by the Normal (or Gaussian) distribution. The Gaussian dis- tribution is symmetric, so deviation from the „average" to both directions has similar properties.

The family of „long tail" or „heavy tail" distributions is well known in statistics. These distributions are skew. Skewness is a measure of asymmetry of a distribution. Some social systems show striking skew distributions. Income distribution, occurrence of words, web hits, copies of books sold, frequency of familiy names are characteristic examples.

Readings:

CE 6.1.1, 6.1.2, 6.2, 6.3.1

8. NETWORKS EVERYWHERE: FROM MOLECULAR to SOCIAL

Topics:

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.' Small world graphs (and also scale-free graphs) are particular examples of complex networks: they are neither purely regular, nor purely random.

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, bioinformatic and scientific collaboration networks will be analyzed.

Readings:

CE 7.4

Péter Érdi: Complex (not only neural) network

http://www.kzoo.edu/physics/ccss/material.html

(A more advanced reading:

Newman MEJ: The structure and function of complex networks)

http://aps.arxiv.org/abs/cond-mat/0303516/

http://geza.kzoo.edu/~csardi/module/html/

9. IN THE INTERSECTION OF DISCIPLINES: HOW TO WIDENING THE LIMITS TO PREDICTIONS?

Epileptics Seizures, Earthquake Eruptions and Stock Market Crashes

-Extreme events: phenomenology

-How to characterize statistically „extreme events”?

-Dynamical models of extreme events: self-organized criticality vs intermittent criticality?

Readings:

CE 9.3.

10. COMPLEXITY RESEARCH: WHERE WE ARE NOW?

Summary

Reports on the group projects

Preparation for the exam.