NONLINEAR DYNAMICS
| Title | ΜΗ-ΓΡΑΜΜΙΚΗ ΔΥΝΑΜΙΚΗ / NONLINEAR DYNAMICS |
| Code | ΜΥΠ731 |
| Faculty | Sciences |
| School | Physics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Spring |
| Common | No |
| Status | Active |
| Course ID | 40000196 |
| Academic Year | 2018 – 2019 |
| Class Period | Spring |
| Faculty Instructors |
|
| Instructors from Other Categories | |
| Weekly Hours | 3 |
| Class ID | 600133668
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600133668
- Other: www.efi-meletlidou.com
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Knowledge in Mathematics and Physics
Learning Outcomes
Knowledge of nonlinear systems and some of their numeruous applications in Physics and biology.
General Competences
- Apply knowledge in practice
- Work autonomously
- Work in teams
- Advance free, creative and causative thinking
Course Content (Syllabus)
flows and mappings, state space, invariant sets equilibrium points of flows and fixed points of mappings
Linearized system stability and invariant manifolds
Local bifyrcations of equilibrium points and fixed points. saddle-node bifurcation, transcritical,pitchfork. Hopf
chaos, definition of chaos chaotic invariant sets, chaotic atractors
Homoclinic and heteroclinic orbits, Melnikov's theory Smale horseshoe
Fractals, Julia sets the mandelbrot set fractal dimention
Applications of nonlinear systems
Logistic map
Epidemiology model
Lorenz equations
Duffing's equation
Josephson junctions
Keywords
Nonlinear systems, chaos
Educational Material Types
- Notes
- Slide presentations
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
Description
Programs in Mathematica
e-mails
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Total | 39 | 1.3 |
Student Assessment
Description
Problems for solution, presentation of a project
Student Assessment methods
- Performance / Staging (Summative)
- Written Exam with Problem Solving (Formative)
Bibliography
Additional bibliography for study
Steven H. Strogatz Nonlinear dynamics and chaos Perseus publishing
Devaney An introduction to chaotic dynamical systems Addison Wesley
John Guckenheimer, Philip Holmes Nonlinear oscillations, Dynamical systems and bifurcatios of vector fields Springer-Verlag
Last Update
20-09-2013
