Subsections
[Cr:4, Lc:2, Tt:0, Lb:3]
Different classes of models of spatiotemporal phenomena will be investigated in this course. Emphasis will be on hands-on implementation of these models in computer programs.
- Cellular Automata Models: basic framework and specific examples such as models of spreading of infectious disease and sandpile models of self-organized criticality.
- Oscillator Chains: basic framework and specific examples (e.g. the Kuramoto model of phase oscillators); synchronization phenomena in such coupled systems.
- Coupled Map lattices: pattern formation in this class of model systems; characterization of correlations in space and time.
- Complex Networks: small-world networks; scale-free networks;
hierarchical networks; modular networks.
- K. Kunihiko, Overview of Coupled Map Lattices, Chaos, vol. 3 (1992) 279.
- M. E. J. Newman, The Structure and Function of Complex Networks, SIAM
Review 45, 167-256 (2003).
- J. A. Acebroen, L. L. Bonilla, C. J. Perez Vicente, F. Ritort, and R.
Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena,
Rev. Mod. Phys. vol. 77 (2005) 137.
- Bak, P., Tang, C. and Wiesenfeld, K., Self-organized criticality: an
explanation of 1/f noise. Physical Review Letters, vol. 59 (1987) 381.
