Modeling Complex Systems

Synchronization in fireflies, schooling in fish, and formation of snowflakes are all examples of complex patterns that emerge from a large number of components interacting through simple rules. These patterns arise in the absence of a central control and continue to do so even if existing components are removed or new ones are added. In this course, we will use mathematical models to understand the rules that give rise to such patterns. Starting with the motivation on why we should model anyway, we will simulate examples of complex systems using methods from population dynamics, self-propelled particles, networks, and cellular automata. The course will consist of weekly lectures and labs, and a final project where you will get to model a system of your choice. Knowledge of undergraduate level calculus, linear algebra, and basic programming (preferably in MATLAB) is required. The objective of this course is to help the student better understand the emergence of complexity in nature and the intuition to take a first crack at modeling a complex system.

- Ability to simulate a complex system and suggest new tools for visualization and analysis
- Understand the global effects of individual and interaction parameters in group behavior
- Knowledge of seminal works and popular models in complex systems
- Ability to abstract a complex system into a simple mathematical form using meaningful assumptions