Dynamic Models in Social Sciences
2006 Winter
Instructor: Péter Érdi, Henry R. Luce Professor
Office: OU 208/B.
Email: perdi@kzoo.edu
TA: Tamás Kiss, PhD
Office: OU 307.
Email: Tamas.Kiss@kzoo.edu
Topics: Mathematical
Goal: The first goal is to teach
WHY mathematical and computational methods are important in
understanding social phenomena, and HOW different social phenonemena
an be described by proper mathematical models. Specifically,
applications of the theory of dynamic systems will be presented.
The course needs some mathematical skill and
background, but teaches and uses the basic mathematical notions of
dynamical system theory. Students of science majors (with some
mathematical interest and skill) are expected to take the
class. Social scientists with some interest to modeling are
welcome.
Course Structure:
Ten topics will be discussed. We shall spend one
week on each topic. During the term it will be possible to attend
demonstrations and make reports on readings. In addition, small groups
will be formed to work on specific projects. They should collect
data, and run simulations.
General Reading:
Epstein, JM: Nonlinear Dynamics, Mathematical
Biology, and Social Science. Santa Fe Inst. Studies in the Science of
Complexity, 1997
Exam:
There will be a sixty minutes long midterm
and a final oral examination. Written and oral report on a group
project is a prerequirement of making the final examination.
Extra-class activities in connection with modeling
and simulation of social systems (e.g. writing of simulation programs,
participation in class discussion, active participation in the
demonstrations of simulation softwares organized by the Center for
Complex System Studies) will also be considered in assigning your
final grade.
1. FROM MATHEMATICAL BIOLOGY TO SOCIODYNAMICS
- Elements of dynamic system theory.
- Basic model frameworks: the population dynamics of cooperation and
competition; models of epidemics.
2-3. MODELS OF COMBAT AND ARMS RACE DYNAMICS
- Lanchaster equation, and its variations. An adaptive combat model.
- Richardson model, and its variations.
Readings:
4. THE PROPAGATION OF IDEAS AND OPINIONS
- The use of epidemic models for modeling the propagation of
revolutionary ideas.
- Temporal and spatiotemporal models.
5. MODELS OF DRUG PROPAGATION AND CONTROL
6. SOCIAL NETWORKS: STATISTICAL ANALYSIS AND DEVELOPMENTAL
MODELS
- Dynamics of attidue change. Dynamic of opinion formation.
- Sprott,
JC: Dynamical Models of Love. Nonlinear Dynamics, Psychology, and Life
Sciences 8(303-314)2004
- Sprott,
JC: Dynamical Models of Happiness, Nonlinear Dynamics, Psychology, and
Life Sciences 9, 23-36 (2005)
- J.A. Hoyst,
K. Kacperski and F. Schweitzer: Social impact models of opinion
dynamics Annual Review of Comput. Phys. 9, 253-273(2001)
7. SOCIAL NETWORKS: STATISTICAL ANALYSISIS AND DEVELOPMENTAL
MODELS
- Social network analysis: searching and finding for the patters of
people's interaction.
- Regular, random and "small world" graphs
- Formal models od network formation. More realistic models.
Readings:
8-9. DYNAMICAL MODELS IN ECONOMICS and POLITICAL SCIENCE
- Chaos and chaos control in economic systems.
- Econophysics.
- Feedback in political science.
- Differential eqautionws versus agent-based models.
Readings:
10. DYNAMICS OF SOCIAL SYSTEMS: WHERE WE ARE NOW?
Summary. Reports on the group projects. Preparation for the exam.
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