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This page was created at 4:32 PM on Fri, Mar 22, 2002.
Open courses in Complex Systems
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Wolverine Access Subject listing for CMPLXSYS
Winter Academic Term '02 Time Schedule for Complex Systems.
CMPLXSYS 510 / MATH 550. Introduction to Adaptive Systems.
Section 001 – Introduction to Dynamical Systems for Biocomplexity.
Prerequisites: Permission of instructor. Working knowledge of calculus, probability, and matrix algebra. (3).
Course Homepage: http://precisione.physics.lsa.umich.edu/CSCS/education/CSCS-courses/cscs510-w01.html
- Linear difference and differential equations on R1
Applications: population growth and finance.
- Second order linear difference and differential equations on R1
Applications: spring, pendulum, Fibonacci systems.
- Nonlinear differential equations on R1 and their phase diagrams
Applications: populations with carrying capacity, infection transmission.
- Linear differential equations in R2. Solution via eigenvalues and phase diagrams
Applications: populations, combat models.
- Nonlinear systems of differential equations
Applications: competing species systems, epidemiology.
- First integrals and Lyapunov functions
Applications: Predator-prey systems, classical physics, HIV transmission.
- Periodic orbits: Poincare-Bendixson Theorem, Bendixson-duLac Criterion, Hopf Bifurcation
Applications: More complex predator-prey models.
- Linear difference equations in Rn. Solution by eigenvalues
Application: Age-structured population models.
- Positive matrices; Perron-Frobenius Theorem
Application: Markov processes in biology and business
Application: Leontieff input-output macroeconomic models.
- Nonlinear difference equations in R1 and Rn. Steady states and their stability
Applications: Population interactions, Newton's Method.
- Chaotic dynamics
Applications: Populations and economies.
- Nonlinear methods of empirical analysis: distinguishing deterministic chaos from randomness
Application: economic and biological data sets.
- Cellular Automata: definition, examples in R1 and R2
Application: population models over time and space, Game of Life.
- Theory and simulation of one-dimensional cellular automata
Applications: plant and animal growth.
- Zero-sum games; Nash equilibria; mixed strategies
Applications: market interactions, poker.
- Non-zero sum games: 2x2 classification, Prisoner's dilemma (one-time and repeated)
Applications: population and market interactions, economic competition.
- Dynamics in non-zero sum games; replicator dynamics and Evolutionarily Stable Strategies
Applications: economics and evolution.
- Introduction to linear partial differential equations (PDEs)
Applications: populations parameterized by age or location, cellular automata.
- Stochastic dynamic systems
Application: birth-death processes in population models,
Application: PDEs for probability generating functions.
- Introduction to Genetic Algorithms
PREREQUISITES: At least one solid course in calculus, familiarity with simple probability.
STUDENTS: Students in biology, economics, political science, natural resources who have minimal math training and would like to learn some mathematical techniques that are commonly used in building and studying models in their fields. This is also the entry course for students in the certificate in complex systems.
CMPLXSYS 530. Computer Modeling of Complex Systems.
Prerequisites: Enrollment in certificate program or permission of instructor. (3).
Course Homepage: http://precisione.physics.lsa.umich.edu/CSCS/education/CSCS-courses/cscs530/W01/index.html
The purpose of this course is to introduce students to the basic concepts, tools and issues which arise when using computers to model
complex (adaptive) systems (CAS). The emphasis will be on agent-based, bottom-up computer models. (We will only briefly look at other
approaches.) The bulk of the course will involve "learning by example", i.e., students will:
- read, discuss, evaluate a number of models from a variety of disciplines.
- Modify and run experiments with existing models.
- Design, implement, run, write-up results from their own models.
The course will cover all aspects of the modeling process itself, from model design through implementation to analyzing, documenting, and
The emphasis in CSCS 530 is on "Exploratory Models" of more generic complex (adaptive) systems and/or phenomena (vs. "predictive"
models for specific situations).
Classwork and grades.
Projects and their influence on a course-grade are as follows:
- Class discussion 20% (An incentive to read and discuss!)
- Short paper 20%
- Small computer modeling project(s) 20%
- Term project 40%
- Proposal (5%)
- Class Presentation (5%)
- Paper (30%)
CMPLXSYS 599. Independent Study of Complex Systems.
Prerequisites: Graduate standing and permission of instructor. (1-3). (INDEPENDENT).
Course Homepage: No homepage submitted.
Directed readings or research in consultation with a member of the faculty in Complex Systems.
This page was created at 4:32 PM on Fri, Mar 22, 2002.
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