GRADUATE SCHOOL
M.SC. in Electrical and Electronics Engineering (With Thesis)
EEE 612 | Course Introduction and Application Information
| Course Name |
Chaos and Fractals
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
EEE 612
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
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| Course Language |
English
|
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| Course Type |
Elective
|
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| Course Level |
Third Cycle
|
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| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | - | |||||
| Assistant(s) | - | |||||
| Course Objectives | The course aims the students: i) to know basic concepts on chaotic systems and fractal sets and ii) to use this knowledge in engineering applications. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | A unification of chaotic dynamics and fractal sets in a dynamical system and set theory background. Sensitive dependency and topological transitivity in invariant sets. From stable fixed points to period doubling, and entrance to chaos. Symbolic dynamics and examples for strange attractors. From cantor set to classical fractals. Self-similarity and fractal dimension. Image encoding by iterated function systems. Randomness in fractal construction. Chaotification. Engineering applications of chaos and fractals. |
|
|
Core Courses | |
| Major Area Courses |
X
|
|
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Historical remarks. First examples of chaotic systems and fractal sets in nature and engineering. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 2 | Nonlinear dynamics: From equilibrium to chaos. Multiple equilibria. Limit cycle. Quasi periodic trajectories. Almost periodicity. Period doubling. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 3 | Definition of chaos. Invariant set. Sensitive dependence on initial conditions. Denseness of periodic and aperiodic trajectories. Topological transitivity. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 4 | Liapunov exponents. Identification of chaos by numerical methods. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 5 | Analysis of discrete time chaotic systems: Logistic map. Fixed point. Contraction mapping. Bifurcation. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 6 | Analysis of continuous time chaotic systems: Lorenz system. Circuit realizations of Lorenz system. Rössler system. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 7 | Chua’s chaotic circuit and its hardware realizations | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 8 | Bifurcation: Pitchfork, saddle-node, Hopf, homoclinic and heteroclinic bifurcations. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 9 | 1. Midterm | |
| 10 | Fractal set examples from nature. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 11 | Definition of fractal set. Self-similarity. Fractal dimension. Box counting dimension. Hausdorff dimension. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 12 | Construction of fractal sets by Iterated Function Systems. Contraction mapping. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 13 | 2. Midterm | |
| 14 | Engineering applications of chaotic systems. Secure communication by synchronized chaotic systems. Chaotification. Chaotic liquid mixing. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 15 | Engineering applications of fractal sets. Fractal image compression. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. |
| 16 | Review of the Semester |
| Course Notes/Textbooks | The textbook referenced above and lecture notes |
| Suggested Readings/Materials | Related Books and Research Papers |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments |
2
|
10
|
| Presentation / Jury | ||
| Project |
2
|
30
|
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
2
|
30
|
| Final Exam |
1
|
30
|
| Total |
| Weighting of Semester Activities on the Final Grade |
70
|
|
| Weighting of End-of-Semester Activities on the Final Grade |
30
|
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
15
|
3
|
45
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
2
|
15
|
30
|
| Presentation / Jury |
0
|
||
| Project |
2
|
20
|
40
|
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
15
|
30
|
| Final Exam |
1
|
32
|
32
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | Accesses information in breadth and depth by conducting scientific research in Electrical and Electronics Engineering; evaluates, interprets and applies information | X | ||||
| 2 | Is well-informed about contemporary techniques and methods used in Electrical and Electronics Engineering and their limitations | X | ||||
| 3 | Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines | X | ||||
| 4 | Is informed about new and upcoming applications in the field and learns them whenever necessary. |
X | ||||
| 5 | Defines and formulates problems related to Electrical and Electronics Engineering, develops methods to solve them and uses progressive methods in solutions. | X | ||||
| 6 | Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs. | X | ||||
| 7 | Designs and implements studies based on theory, experiments and modeling; analyses and resolves the complex problems that arise in this process. | X | ||||
| 8 | Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility. | X | ||||
| 9 | Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale. | X | ||||
| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. | X | ||||
| 11 | Is knowledgeable about the social, environmental, health, security and law implications of Electrical and Electronics Engineering applications, knows their project management and business applications, and is aware of their limitations in Electrical and Electronics Engineering applications. | X | ||||
| 12 | Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. Adheres to the principles of research and publication ethics. |
X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest