Instructor Information

Daniel Wiley

Daniel Wiley holds BS degrees in Mathematics and Physics from Portland State University and a PhD in Applied Mathematics from Cornell University. He specialized in complex systems and worked for two summers as an instructor at the Mathematical and Theoretical Biology Institute. Dr. Wiley held academic positions at Howard University, the Mathematical Sciences Research Institute, and the University of Maryland, College Park. Dr. Wiley currently reviews potential publications for the journal CHAOS. He is presently employed as a mathematician for the U.S. Government.

Course Information

Course Description

This multi-disciplinary course focuses on the application of modeling and simulation principles to complex systems. A complex system is a large-scale nonlinear system consisting of interconnected or interwoven parts (such as a biological organism, an ecological system, the economy, fluids or strongly-coupled solids). The subject is interdisciplinary with foundations in mathematics, nonlinear science, numerical simulations and statistical physics. The course begins with an overview of complex systems, followed by modeling techniques based on nonlinear differential equations, networks, and stochastic models. Simulations are conducted via numerical calculus, analog circuits, Monte Carlo methods, and cellular automata. In the course we will model, program, and analyze a wide variety of complex systems, including dynamical and chaotic systems, cellular automata, and iterated functions. By defining and iterating an individual course project throughout the term, students will gain hands-on experience and understanding of complex systems that arise from combinations of elementary rules. Students will be able to define, solve, and plot systems of linear and non-linear systems of differential equations and model various complex systems important in applications of population biology, epidemiology, circuit theory, fluid mechanics, and statistical physics.Course prerequisite(s): Knowledge of elementary probability and statistics and previous exposure to differential equations. Students applying this course to the MS in Bioinformatics should also have completed at least one Bioinformatics course prior to enrollment.Course note(s): This course may be counted toward a three-course concentration in Bioinformatics.

Course Goal

In this course, we will model, program, and analyze a wide variety of complex systems, including dynamical and chaotic systems, cellular automata, fractals, and iterated functions. 

Matlab will be used for simulation demonstrations.  Students will also do a project on a topic of interest, which may be coded in any language of the student's choice.

Students wishing to obtain credit in Bioinformatics may choose a topic with biological content for the project.

Course Objectives

  • Gain an understanding of qualitative techniques for analyzing nonlinear differential equations.
  • Define and analyze chaotic systems.
  • Simulate several complex systems models using numerical analysis and cellular automata.
  • Complete a course project throughout the term for a complex system relevant to the student.

When This Course is Typically Offered

This course is typically offered in the spring at APL.


  • phase space methods
  • bifurcations
  • numerical simulations
  • limit cycles
  • chaos
  • phase transitions
  • cellular automata
  • iterated functions

Student Assessment Criteria

Midterm Exam 33%
Project 33%
Final Exam 33%
Homework (max) 10%

We will invest some class time in proposing and discussing class projects that hopefully will be in line with students' interests and will be fun and interesting!

Computer and Technical Requirements

Students are expected to have some experience in computer programming.   Demonstrations will be given using the Matlab programming language.  For homework and projects students may use any programming language.

Participation Expectations

The course will be a mix of theory and computers simulations.  A portion of the class meetings will be dedicated to discussing and developing the course project.


Textbook information for this course is available online through the MBS Direct Virtual Bookstore.

Course Notes

There are no notes for this course.

Final Words from the Instructor

Modeling and Simulation of Complex Systems is now featured at
Computer Science Course Spotlight!

[At the Computer Science Home Page, a link to the Course Spotlight video is on the left.]

The required texts for this course are Nonlinear Dynamics and Chaos by Steven Strogatz and Introduction to the Modeling and Analysis of Complex Systems by Hiroki Sayama.  There is also an optional text Dynamical Systems with Applications using MATLAB by Stephen Lynch.  Electronic versions of all three texts are available for download through Taylor and Francis and SpringerLink via the JHU Library and Open SUNY Textbooks.  

Term Specific Course Website

(Last Modified: 12/09/2021 10:25:10 AM)