COURSE UNIT TITLE

: CHAOS THEORY

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
ELECTIVE

Offered By

Physics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR GÜL GÜLPINAR

Offered to

Physics

Course Objective

Audience of the course is undergraduate student in the 4th semester. The students who successfully complete the lecture will gain fundamental background on non-linear dynamics and chaotic system.

Learning Outcomes of the Course Unit

1   To learn the relation between linear, non-linear systems and chaos.
2   To understand the universal aspects of chaos theory.
3   To gain the knowledge on the concepts of attractors, limit cycles and state spaces.
4   To model numerically the iterated maps
5   To learn the measuring tools and qualitative properties of chaos.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Dynamic systems: Properties of discrete and continuous systems 1
2 Dynamic systems: Autonomous and non- autonomous systems, phase portraits and flows 2
3 Linear and non-linear systems: electrical circuits, biological population growth model, Lorentz model 3
4 Determinism, unpredictability, and divergent trajectories 4
5 Universality of chaos 5
6 Dynamics of state space in 1D and 2D systems 6
7 Problem solving 7
8 Iterated maps: bifurcations, periodic doubling, chaos and Lyapunov exponents 8
9 Lyapunov exponents continued 9
10 Iterated maps:Feigenbaum universality, 1D maps 10
11 Iterated maps: 2D maps 11
12 Measuring chaos: Lyapunov exponents, Kolmogorov-Sinai entropy, fractal dimension 12
13 Mesuring chaos continued 13
14 General review 14

Recomended or Required Reading

Main reference textbook:
Chaos and nonlinear Dynamics, An introduction for scientists and engineers, Second Edition, Robert C. Hilborn, Oxford University Press

Auxiliary textbook
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition (Studies in Nonlinearity), S. H. Strogatz, Second Edition,
Material:
Applied nonlinear Dynamics: Analytical, Computational, and Experimental Methdos, A. Nayfeh, B. Balachandran, Wiley Series in Nonlinear science

Chaos and integrability in nonlinear Dynamics: An introduction, M. Tabor, Wiley and Sons

Planned Learning Activities and Teaching Methods

Lectures, problem solving and discussion, Tutorials and homeworks

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.30 + ASG * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + ASG * 0.30 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

The student s performance will be determined according to the midterm and final exam grade, as well as to the homework assigments.

Language of Instruction

Turkish

Course Policies and Rules

1. Attending at least 70 percent of lectures is mandatory.
2. Plagiarism of any type will result in disciplinary action.

Contact Details for the Lecturer(s)

yusuf.yuksel@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 2 28
Tutorials 14 2 28
Preparations before/after weekly lectures 14 2 28
Preparation for midterm exam 1 16 16
Preparation for final exam 1 16 16
Preparing assignments 4 8 32
Midterm 1 3 3
Final 1 1 1
TOTAL WORKLOAD (hours) 152

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.155554444353222
LO.255554444353222
LO.355554444353222
LO.455554444353222
LO.555554444353222