Coursebooks

Dynamics and bifurcation

MATH-325

Lecturer(s) :

Vela Arevalo Luz Vianey

Language:

English

Summary

Introduction to local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations. Theoretical and computational aspects studied.

Content

One dimensional flows

Elementary bifurcations

One dimensional maps

Systems of ordinary differential equations: planar systems and phase portraits, non linear systems, Lyapunov stability, mechanical systems, La-Salle invariance principle, index in two dimensional vector fields, periodic orbits and limit cycles, Poincaré-Andronov-Hopf bifurcation, structural stability.

Keywords

Systèmes dynamiques à temps discrets et à temps continu, discrete and continuous dynamical systems, elementary bifurcations: saddle-node, transcritical, hysteresis, pitchfork; Lyapunov stability, Poincaré maps, mechanical systems.

Learning Prerequisites

Required courses

Analyse I, Analyse II, Algebre linéaire

Recommended courses

Equations différentielles ordinaires

Learning Outcomes

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

Transversal skills

Teaching methods

Lectures 2 hours a week and exercise sessions 2 hours a week.

Expected student activities

Attendance to lectures, attendance to exercise sessions, solution of homework problems that may involve theoretical or numerical solutions, give a final exam.

Assessment methods

Final exam.

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés

Supervision

Office hours No
Assistants Yes
Forum Yes

Resources

Bibliography

Introduction to Dynamical Systems: continuous and discrete, by Clark Robinson, 2012.

Dynamics and bifurcations, by J. Hale and H. Kocak, 1991.

Ressources en bibliothèque
Notes/Handbook

Lecture notes will be given, to be completed by the students.

Websites

In the programs

  • Mathematics, 2019-2020, Bachelor semester 6
    • Semester
      Spring
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Dynamics and bifurcation
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German