Complex Systems
None - but it would be useful if you had attended the Fractals &
Chaos and/or the Nonlinear Waves courses.
Definition and examples of complex systems
and basic concepts used to describe them; types and examples of
cellular automata; mean-field approximation; percolation theory;
graph theory; types of network; robustness of networks; dynamical
systems on networks;
origin of scaling laws; game theory;
neural networks; genetic algorithms; complex adaptive systems.
By the end of the course students should be able to:
- understand the concepts listed in the detailed syllabus
- characterize elementary cellular automata and the
patterns that occur as they evolve
- apply the mean-field approximation to cellular automata
- calculate simple properties of graphs
- classify networks
- analyse simple dynamical systems on networks
- Week 1
- Definition and examples of complex systems
and basic concepts: course-graining; order parameter; control parameter;
emergence; symmetry breaking; annealing; quenching; topological
defect; measures of complexity
- Week 2
- Cellular automata (CA): types and examples of CA
- Week 3
- Mean-field approximation
- Week 4
- Percolation theory
- Week 5
- Graph theory: definitions, quantifiable properties, matrices
describing graphs
- Week 6
- Types of network
- Week 7
- Robustness of networks
- Week 8
- Exam 1 (on weeks 1-7)
- Week 9
- Dynamical systems on networks
- Week 10
- Origin of scaling laws
- Week 11
- Introduction to game theory; minority games: El Farol bar problem
- Week 12
- Neural networks: Hopfield network, energy function
- Week 13
- Genetic algorithms
- Week 14
- Complex adaptive systems
- Week 15
- Selected topics of current interest
- Week 16
- Selected topics of current interest
- Week 17
- Exam 2 (on weeks 1-16)
Lectures and detailed printed lecture notes will be provided.
Homework: 4%
Exam 1: 48%
Exam 2: 48%
- C. Gros, "Complex and Adaptive Dynamical Systems: A Primer",
Springer, 2011.
- M.E.J. Newman, "Networks: An Introduction", OUP, 2010.
2016-07-11
