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
The course consists of three parts.
Part 1: Nonlinear dynamics
- One-dimensional and two-dimensional systems, phase-plane analysis, elementary bifurcations, limit cycles, and Hopf bifurcations
Part 2: Chaos
- Lorenz system and chaotic dynamics
- Iterated maps, period-doubling, chaos, universality
- Fractals
- Strange attractors
Part 3: Introduction to complex systems
- The science of complexity
- Examples of complex systems, networks, 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:
- 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
In the programs
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Nonlinear dynamics, chaos and complex systems
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Nonlinear dynamics, chaos and complex systems
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Nonlinear dynamics, chaos and complex systems
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Nonlinear dynamics, chaos and complex systems
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional