College of LS&A

Winter Academic Term '02 Graduate Course Guide

Note: You must establish a session for Winter Academic Term 2002 on in order to use the link "Check Times, Location, and Availability". Once your session is established, the links will function.

Courses in Complex Systems

This page was created at 4:32 PM on Fri, Mar 22, 2002.

Winter Academic Term, 2002 (January 7 - April 26)

Open courses in Complex Systems
(*Not real-time Information. Review the "Data current as of: " statement at the bottom of hyperlinked page)

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.

Instructor(s): Carl P Simon (

Prerequisites: Permission of instructor. Working knowledge of calculus, probability, and matrix algebra. (3).

Credits: (3).

Course Homepage:

  • 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.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

CMPLXSYS 530. Computer Modeling of Complex Systems.

Section 001.

Instructor(s): Rick L Riolo (

Prerequisites: Enrollment in certificate program or permission of instructor. (3).

Credits: (3).

Course Homepage:

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:

  1. read, discuss, evaluate a number of models from a variety of disciplines.
  2. Modify and run experiments with existing models.
  3. 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 communicating results.

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:

  1. Class discussion 20% (An incentive to read and discuss!)
  2. Short paper 20%
  3. Small computer modeling project(s) 20%
  4. Term project 40%
    1. Proposal (5%)
    2. Class Presentation (5%)
    3. Paper (30%)

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 1

CMPLXSYS 599. Independent Study of Complex Systems.


Prerequisites: Graduate standing and permission of instructor. (1-3). (INDEPENDENT).

Credits: (1-3).

Course Homepage: No homepage submitted.

Directed readings or research in consultation with a member of the faculty in Complex Systems.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

Undergraduate Course Listings for CMPLXSYS.

Page Counter

This page was created at 4:32 PM on Fri, Mar 22, 2002.

lsa logo

University of Michigan | College of LS&A | Student Academic Affairs | LS&A Bulletin Index | Department Homepage

This page maintained by LS&A Academic Information and Publications, 1228 Angell Hall

Copyright © 2001 The Regents of the University of Michigan,
Ann Arbor, MI 48109 USA +1 734 764-1817

Trademarks of the University of Michigan may not be electronically or otherwise altered or separated from this document or used for any non-University purpose.