COURSE UNIT TITLE

: NONLINEAR DYNAMICS AND CHAOS-I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5135 NONLINEAR DYNAMICS AND CHAOS-I ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ÜMIT AKINCI

Offered to

PHYSICS
PHYSICS

Course Objective

This course provides an introduction to the theory and phenomenology of nonlinear
dynamics and chaos in dissipative systems and the methods for the identification of nonlinear systems used other model structures such as Volterra and Wiener models, NARMAX modeIs and neural Networks.

Learning Outcomes of the Course Unit

1   Explore the basic concepts of nonlinear dynamics
2   Be able to model new physical situations using the methods exemplified in the course.
3   Be able to analyse simple one and two-dimensional nonlinear systems
4   Have gained insights into more advanced methods which touch upon modern research.
5   Be able to identify attractors of those nonlinear systems, and to characterise their stability.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Introduction
2 Pendulum and Stability of Solutions to ODEs
3 Damped Oscillators and Dissipative Systems and Forced Oscillators and Limit Cycles
4 Parametric Oscillator and Fourier Transformations-1
5 Fourier Transformations-2
6 Fourier Transformations-3 and Poincaré Sections-1
7 Poincaré Sections-2
8 Poincaré Sections-3 and Fluid Dynamics and Rayleigh- Bénard Convection-1
9 Fluid Dynamics and Rayleigh Bénard Convection-2
10 Fluid Dynamics and Rayleigh Bénard Convection-3
11 Introduction to Strange Attractors and Lorenz Equations
12 Lorenz Equations (cont.) and Hénon Attractor

Recomended or Required Reading

Textbook:
S. Strogatz, C.O. Boulder, Nonlinear Dynamics and Chaos. Westview Press, (1994),ISBN:
9780201543445.
References:
1. Baker, G. L., and J. P. Gollub., Chaotic Dynamics, 2nd ed. Cambridge, UK: Cambridge
University Press, 1996. ISBN: 9780521471060.
2. Berge, P., Y. Pomeau, and C. Vidal. Order within Chaos. New York, NY: John Wiley &
Sons, 1987. ISBN: 9780471849674.
3. Beltrami, E. Mathematics for Dynamic Modeling. Boston, MA: Academic Press, 1987.
ISBN: 9780120855551.
4. Gleick, James. Chaos: Making a New Science / James Gleick. New York, NY: Viking,
1987. ISBN: 9780670811786.

Planned Learning Activities and Teaching Methods

1. Lecturing
2.Question-Answer
3.Discussing
4.Homework

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria


1. The homework and mid-term exams of the student is assessed as the achievement of them in the semester.
2. At %40 score of final examination is added directly to the others.

Language of Instruction

English

Course Policies and Rules

1. It is obligated to continue at least 70% of lessons.
2. If the student don t make the homework and attend mid-terms, he does not access the final exam

Contact Details for the Lecturer(s)

gul.gulpinar@deu.edu.tr

Office Hours

Wednesday and Friday between at 11:00-12:00 a.m.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lecture 14 3 42
Weekly preparations before/after course 14 4 56
Preparations for mid-term exam 1 5 5
Preparations for final exam 1 10 10
Preparations for homework 8 7 56
Final Exam 1 3 3
Mid-term Exam 2 2 4
TOTAL WORKLOAD (hours) 176

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.14335544345
LO.25434433435
LO.34434533345
LO.45533543335
LO.55434544444

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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