Continuous and discrete dynamical systems. Fixed points. Bifurcations. Chaos.
Discrete maps. Pattern formation in reaction diffusion systems. Introduction to stochastic process. Markov chain and applications. Langevin and Fokker-Planck. First passage time and Arrhenius theory, network theory, applications.
1) Steven Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press 1994, ISBN-13: 9780738204536
2) Crispin W. Gardiner, Handbook of Stochastic Methods, Springer 2009, ISBN-13: 9783540707127
3) James D. Murray, Mathematical Biology: an Introduction. Springer.
4) R. Livi, P. Politi Nonequilibrium Statistical Physics: A Modern Perspective, Cambridge University Press (2017)
Learning Objectives
The course aims at providing an overview of the physics of complex systems, and elaborate on its diverse applications to distinct fields (physics, chemistry, biology ecology).
Prerequisites
-Basic knowledge of physics
-Differential calculus in several variables, differential equations.
The course aims at providing a first introduction to students interested in dynamical systems and complex systems.
Teaching Methods
Lectures and computer examples.
Type of Assessment
Carry our a project (with a numerical and or analytical part) and present it during an oral session.
Course program
Continuous and discrete dynamical systems. Fixed points. Bifurcations. Chaos.
Discrete maps. Pattern formation in reaction diffusion systems. Introduction to stochastic process. Markov chain and applications. Langevin and Fokker-Planck. First passage time and Arrhenius theory, network theory, applications.