Nonlinear dynamics, chaos and complex systems

Summary

The course provides students with the tools to approach the study of nonlinear systems and chaotic dynamics. Emphasis is given to concrete examples and numerical applications are carried out during the exercise sessions.

Content

Keywords

Chaos, Nonlinear systems, Complex system, Fractals, Differential equations, Bifurcations.

Learning Prerequisites

Required courses

Introductory Physics and Math courses. 

Learning Outcomes

By the end of the course, the student must be able to:

• Manipulate the fundamental elements of nonlinear systems and chaotic dynamics

Teaching methods

Ex cathedra and exercises in class.

Assessment methods

Oral Exam

Resources

Bibliography

- S.H. Strogatz, Nonlinear dynamics and chaos, with application to Physics, Biology, Chmistry, and Engineering, Second Edition, Westwiew Press.

- P.G. Drazin, Nonlinear systems, Cambridge University Press.

- M.W. Hirsch, S. Smale, and R.L. Devaney, Differential equations, dynamical systems, and an introduction to chaos, Elsevier.

- M. Dichter, Student solutions manual for Nonlinear dynamics and chaos, Westview Press.

Ressources en bibliothèque

• M.W. Hirsch, S. Smale, and R.L. Devaney, Differential equations, dynamical systems, and an introduction to chaos, Elsevier.
• Strogatz / Nonlinear dynamics and chaos
• Drazin / Nonlinear systems
• Dichter / Nonlinear dynamics and chaos - Student solution

Moodle Link

• https://go.epfl.ch/PHYS-460