1. MEE428/MEE528 – Modeling Complex Systems

Fall 2017

Course (catalog) description

Graph theory, network models, mean field approximation, phase portraits, bifurcation diagrams, in-formation theory, and game theory. Modeling of disease/rumor spread, self-propelled particle systems,socio/economic networks, power grids, multi-agent robotic systems, coupled-oscillator dynamics, andself-repeating patterns such those find in ant nests, disease tumors, and vehicular traffic.

Long description Complex systems are best identified by unpredictable, and sometimes fascinating,phenomena they exhibit when simple things come together. Examples include synchronization infireflies, schooling in fish, and formation of snowflakes. We call these systems complex because a largenumber of components interact through a simple set of rules to give rise to unpredictable patterns.Such simple interactions are thought to be the basis for intelligence and complex systems in nature haveinspired swarm robotics and particle swarm optimization. In this course, we will use mathematicalmodels to visualize patterns arising in complex systems and isolate the key drivers of the final outcomes.We will begin with the motivation on why we should model anyway, and go on to simulate real-worldscenarios using methods from population dynamics, self-propelled particles, networks, and cellularautomata. The course will consist of weekly lectures, in-class simulation exercises (labs), and a finalproject where you will model and analyse a system of your choice. Knowledge of ordinary differentialequations, linear algebra, and basic programming (preferably in MATLAB) is required. The objectiveof this course is to help you better understand the emergence of complexity in nature and developingthe intuition to take a first crack at modeling a complex system.1

Course objectives On completing this course, the student will be able to:

• Abstract a complex system into a simple mathematical form using meaningful assumptions (a, e,c)

• Simulate and visualize complex dynamical phenomena including disease spreading, collective be-haviour, vehicular traffic, and social networks (b, k)

• Identify key driving points, properties and vulnerabilities of complex systems that can be used topredict qualitative outcomes (e, g)

2. Prerequisites: MEE 321 or consent of department. This course expects familiarity with calculus(ODE, PDE), linear algebra, and programming in MATLAB. You are strongly advised to use Homework#0 as a way to assess your preparedness for this class. You are expected to have read the pre-assignedmaterial (reading and homework assignments) before coming to the class. You must bring a chargedlaptop to some lectures to try out sample simulations during the lecture.

1top image: map of the internet (wikipedia)

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3. Credit and contact hours: 3 Cr. hrs. Contact hours is one 160 minutes lectures/week

Meeting times

Tue, Thu: 12:30–1:45p, EB209

4. Instructor: Sachit Butail

EB 148Office hours: Mon 10a–12p, Thu 3:00–4:30p, or by appointmentsbutail@niu.edu(815) 753-9987

5. Textbook(s) and/or other required materials:

There is no prescribed text for this course; we will be mainly using class notes and published papers.Lectures will assume that you have come prepared and will focus on answering questions and reinforcingconcepts. Below are suggested texts that you may be use to supplement your learning:

• Sayama H. Introduction to the Modeling and Analysis of Complex Systems Link (SH)

• Boccara N. Modeling complex systems. New York, New York, USA: Springer

• Bullo F. Lectures on Network Systems http://motion.me.ucsb.edu/book-lns/

• Strogatz S. H. Nonlinear dynamics and chaos: with applications to Physics, Biology, Chemistryand Engineering. Cambridge, Massachusetts, USA: Westview Press

• Sumpter D. J. T. Collective animal behavior. Princeton, New Jersey, USA: Princeton UniversityPress

6. Specific Course Information:

i. Homeworks:

There will be three homework assignments as part of this course. MEE528 students will haveadditional homework problems. These are long and you are strongly advised to start them as soonas possible. These will be due as per the schedule (Table 1). You are encouraged to collaborate onthese, however, the work you submit should be entirely your own. No late submissions allowed.

ii. Project:

The course will end with a final project where you are encouraged to model and analyze a complexsystem of your choice, or, review and reproduce the results of a recent paper that models a complexsystem. The project topic or paper must be approved by the end of Week 10. At the end of theproject you will be required to submit a 3 page report (including figures but excluding bibliography,and preferably in LATEX) and present your findings before the class for 10 minutes. A detailed rubricfor project grading will be shared after the midterm exam.

iii. Grading:

• Homework #0: 5% (to be graded by fellow students)

• Homework Assignments (3): 60%

• Project study: 30%

• Class participation: 5% (to encourage reading and discussion)

iv. Note:

• It is your responsibility to check your scores on Blackboard periodically. Scores will only beupdated for the most recent homework/quiz/project/exam.

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7. Specific goals for the course:

Coverage of ABET Outcomes:

a. an ability to apply knowledge of mathematics, science, and engineering

b. an ability to design and conduct experiments, as well as to analyze and interpret data

c. an ability to design a system, component, or process to meet desired needs within realistic con-straints such as economic, environmental, social, political, ethical, health and safety, manufac-turability, and sustainability

e. an ability to identify, formulate, and solve engineering problems

g. an ability to communicate effectively

k. an ability to use the techniques, skills, and modern engineering tools necessary for engineeringpractice.

Table 1: Schedule. Reading assignments, available here and online, must be finished prior to coming to thelecture.

Week Outcome Readings Hwks

1 Why model? What is a dynamical system? Complex system? Mathe-matical preliminaries. How to integrate an ODE?

Why model?, Chapter3 SH

2 Nonlinear systems, phase portraits, chaotic behavior, equilibria, Limitcycles, periodic orbits

Chapter 7 SH 0 due9/4/17

3 Plot the evolution of a dynamical system? What are tipping points?Plot bifurcation diagrams

Chapter 8 SH

4,5 Model dynamics of populations. Mean-field approximation? Examplesfrom disease spread, rumor spread, fads

Logistic growth model,Predator-prey model

1 due9/19/17

6,7 Animal conflict, game theory, Hawk vs Dove, Evolutionarily stablestrategies, pursuit and evasion, applications in robotics

Smith1973

8,9,10

Representing networks using graphs; adjacency matrix, laplacian, Gen-erating random networks, and their properties; compare with real-world networks such as world-wide web, power grid, social networks;Scaling in networks, Cascade attacks on power grids, Measuring com-plexity, Network synchronization

How things in naturetend to sync up, Mil-lenium Bridge, Keel-ing2005

2 due10/17/17

11,12 Model collective motion in nature. Interaction rules giving rise toemergent behavior. Insect swarms, fish schools, bird flocks, inspirationfor multi-robot systems, contagion

Couzin2007, Vic-sek2012

3 due11/14/17

13, 14 How to model cancer spread, traffic flow, patterns on seashells andsnowflakes. What is artificial intelligence

Conway’s game of Life

15 Project presentations

Accessibility Statement

If you need an accommodation for this class, please contact the Disability Resource Center as soon as possible.The DRC coordinates accommodations for students with disabilities. It is located on the 4th floor of theHealth Services Building, and can be reached at 815-753-1303 (V) or drc@niu.edu. Also, please contact meprivately as soon as possible so we can discuss your accommodations. The sooner you let us know yourneeds, the sooner we can assist you in achieving your learning goals in this course.

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Academic Integrity

Please carefully go through http://www.niu.edu/ai/students/. Please discuss with me if you have doubtsabout what constitutes dishonesty, plagiarism, and cheating. You are responsible for your work!

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