PHYS-460 / 6 credits

Teacher: Février Olivier Claude Martin

Language: 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 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.

## 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.

Oral Exam

## 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.

## In the programs

• Semester: Spring
• Exam form: Oral (summer session)
• Subject examined: Nonlinear dynamics, chaos and complex systems
• Lecture: 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
• Lecture: 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
• Lecture: 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
• Lecture: 3 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional

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