Faglærer: Gunnar Tufte, Johannes H. Jensen, Arthur Penty
Students: List

• Startup and first meeting: Monday September 15. at 11:00-12:00 in room 207 in Gamle Fysikk

Description: "The whole is more than the sum of its parts" -- Aristotle  
  
Complex systems are systems where the collective behavior of their parts can not be inferred from the properties of the parts themselves. Examples of complex systems include insect colonies, the Internet, human economies, climate, nervous systems, cells and living things, and human beings.

This course covers theory and important aspects related to the modeling and analysis of complex systems. The knowledge will be useful in scientific pursuits, but also for work in industry and everyday life. It will complement top-down engineering skills with bottom-up techniques.

Keywords: Complex systems, fundamentals of modeling, dynamical systems, phase space, state space, basins of attraction, bifurcations, chaos, nonlinear systems, emergence, self-organization, cellular automata.

Structure: Lectures are organized as discussions on selected chapters from the text book. Before each meeting, the students are expected to read the selected chapters and solve one or more exercises related to the topics. At the meetings, the students will present and discuss their solutions.

Syllabus

Selected chapters from the text book Introduction to the Modeling and Analysis of Complex Systems by Hiroki Sayama. The text book is freely available online.

Session 1: Preliminaries

Chapters:

- 1 Introduction
- 2 Fundamentals of Modeling
- 3 Basics of Dynamical Systems

Exercises: 3.3, 3.4, 3.5, 3.6

Session 2: Discrete-time models

Chapters:

- 4 Discrete-Time Models I: Modeling
- 5 Discrete-Time Models II: Analysis

Exercises: Select one (or more) of the programming exercises from the chapters.

Session 3: Continuous-time models

Chapters:

- 6 Continuous-Time Models I: Modeling
- 7 Continuous-Time Models II: Analysis
- 8 Bifurcations
- 9 Chaos

Exercises: Select one (or more) of the programming exercises from the chapters.

Session 4: Systems with a large number of variables

Chapters:

- 10 Interactive Simulation of Complex Systems
- 11 Cellular Automata I: Modeling
- 12 Cellular Automata II: Analysis

Exercises: Select one (or more) of the programming exercises from the chapters.