In addition to an introduction to chaotic dynamics in both conservative and dissipative systems, the course covers several aspects of nonlinear oscillations, fractal geometry, dynamics of complex systems, and applications. In addition to chaotic dynamics, the course also covers the following topics:
Disorder effects: Sinai walk, Renormalization Group treatment
Anomalous diffusion – various mechanisms
Nonlinear time series analysis
Schramm-Loewner Evolution, CFT
Quantum Chaos
Application: Network Evolution
Application: Nonlinear Dynamics of Networks
Application: Brain dynamics
Main references:
- E. Ott, Chaos in Dynamical Systems (Cambridge Univ. Press, Cambridge, 2002).
- Strogatz, Steven H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Westview Press, 2014. ISBN: 9780813349107.
- chaosbook.org – free resource, with many additional topics, illustrations as well as lecture videos
- Smith, Chaos – A very short introduction (Oxford, 2007)
- Gleick, Chaos – making a new science (Penguin, 1995)
Example student projects from previous classes:
| The use of dynamical systems theory in developing environmental policy |
| Epidemiological Models (Spread of Disease) |
| Chaos theory for cryptography |
| Biological Morphogenesis |
| Social balance in coarse-grained networks |
| Ferromagnetic phase transition |
| Chaos in human physiology (cardiac arrhythmia) |
| Probability density: Time evolution of densities for 1D and 2D maps |
| Chaos in Network Evolution |
| Chaos in Cellular Automata |
| Simulation of a self organizing system – population dynamics |
| Modeling COVID-19 Spread |
| Predicting the double pendulum |
| Control of nonlinear systems |
| Weather and Climate Predictability |
| Network evolution in ecosystem |
| Numerical Simulations of Complex Ginzburg Landau equation |
| Nonlinear time series analysis of electrochemical systems |
| Conway’s Game of Life |
| Chaos/Nonlinear Dynamics in the Stock Market |
| collective human conflict/arms races |
| BZ reaction (Nonlinear chemical oscillators) |
| Link removal strategies for dismantling complex networks |
| Nonlinear Dynamics in the Brain |