Fiches de cours 2018-2019

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Nonlinear dynamics, chaos and complex systems

PHYS-460

Enseignant(s) :

Ricci Paolo

Langue:

English

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

The course consists of three parts.

Part 1: Nonlinear dynamics

- One-dimensional systems and elementary bifurcations

- Two-dimensional systems, phase-plane analysis, limit cycles, and Hopf bifurcations

Part 2: Chaos

 - Lorenz system and chaotic dynamics

- Iterated maps, period-doubling, chaos, universality, and renormalization

- Fractals 

- Strange attractors

Part 3: Introduction to complex systems

-  The science of complexity

-  Examples of complex systems, networks, turbulence, etc. 

 

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:

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
Moodle Link

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14   CM1104 
14-15    
15-16   CM1112 
16-17    
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand