MATH-325 / 5 credits

Teacher: 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.

## 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.

## Required courses

Analyse I, Analyse II, Algebre linéaire

## Recommended courses

Equations différentielles ordinaires

## Learning Outcomes

• Analyze dynamical systems in continue and discrete time
• Describe local and global behavior of differential equations and maps
• Work out / Determine stability properties as a function of one or more parameters

## Transversal skills

• Communicate effectively, being understood, including across different languages and cultures.
• Communicate effectively with professionals from other disciplines.
• Use a work methodology appropriate to the task.

## 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

## Bibliography

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

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

## Notes/Handbook

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

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• 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

 Mo Tu We Th Fr 8-9 9-10 10-11 MAB111 MAA112 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Thursday, 10h - 12h: Lecture MAB111

Friday, 10h - 12h: Exercise, TP MAA112