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
Oral exam organized into two parts: questions on the topics covered during the lectures and a short talk on a specific item, related to the course program, selected by the student. The exams allows one to gauge the basic knowledge on the topics addressed as well as to assess the acquired skills.
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.