COURSE UNIT TITLE

: COMPLEX SYSTEMS-I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5077 COMPLEX SYSTEMS-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

PROFESSOR DOCTOR GÜL GÜLPINAR

Offered to

PHYSICS
PHYSICS

Course Objective

The course provides a broad overview of concepts and methods used in
the field of complex adaptive systems. Methods of dynamical systems
and statistical physics provide the tools for formally describing and
analysing these systems. The collective dynamics are illustrated by
means of computer simulations, mainly using multi-agent approaches

Learning Outcomes of the Course Unit

1   Be aware of simple systems that exhibit nonlinear and complex behaviour
2   Be able to analyse nonlinear systems and find stationary points
3   Posses the ability to analyse bifurcation diagrams and identify key features on these diagrams
4   Understand the origin of deterministic chaos and explain key features relating to chaos
5   Be able to demonstrate an understanding of the algorithms described in the course
6   Have demonstrated the ability to implement stable, efficient and numerically correct versions of these algorithms, with source code which is well documented
7   Develop an ability to decide the reliability and usefulness of derived computational results.
8   Appreciate the physical significance of derived computational results.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Introduction What are complex systems .Why is nonlinear physics is important
2 Predictability, nonlinearity and complexity, bifurcations and universality Examples of 1D nonlinear models (ODEs): population dynamics, lasers etc. Stationary solutions (fixed points).
3 Complex systems in 1D
4 Linear stability analysis Bifurcation diagrams. Transcritical bifurcations. Vector fields. Bistability. Saddle-node bifurcations. Bistability as combination of saddle-node bifurcations
5 Complex systems and oscillations in 2D and 3D Lasers with saturable absorbers
6 Complex systems and oscillations in 2D and 3D (cont.) Eigenvalues and eigenvectors of a system of linear ODEs. Onset of oscillations. Harmonic and nonlinear oscillators, Fourier analysis
7 Complex systems and oscillations in 2D and 3D (cont.) Evolution of perturbations near fixed points. Jacobian matrices. Hopf bifurcations. Stability of periodic orbits
8 Mid term exam
9 Discrete systems Poincaré sections and maps. Stability of maps fixed points. Flip bifurcation and period doubling.
10 Discrete systems (cont.) Period doubling cascade and deterministic chaos
11 Deterministic chaos
12 Deterministic chaos (cont.)
13 Presentation of the projects
14 Presentation of the projects (cont.)

Recomended or Required Reading


Text book:
S. Strogatz, Nonlinear Dynamics and Chaos. Boulder, CO: Westview Press, 1994. ISBN:9780201543445.
References
1. H. J. Jensen (1998), Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems ,Cambridge Lecture Notes in Physics, Cambridge.
2. Weisbuch, Gérard; Ryckebusch, Sylvie (1991), Complex systems dynamics: An introduction to automata networks. Santa Fe Institute studies in the sciences of complexity: Lecture notes, Vol. 2, Addison-Wesley/Addison Wesley Longman, Reading.
3. Edited by Terry R. J. Bossomaier, David G. Green, Complexity Theory (2000), Cambridge University Press , Cambridge.
4. M. S. Garrido, R. V. Mendes (1992), Complexity in Physics and Technology, World Scientific, New York.

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 PRJ PROJECT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE PRJ * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) PRJ * 0.30 + MTE * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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 do not 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

friday between 13:00-15:00

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lecture 11 3 33
project presentations 2 3 6
Preparations for final exam 1 15 15
Preparations for mid-term exam 1 10 10
Preparations for homework 10 4 40
Preparation of the project report representation 1 10 10
Weekly preparations before/after course 13 4 52
Final exam 1 3 3
Mid term exam 1 2 2
TOTAL WORKLOAD (hours) 171

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.15
LO.245343
LO.3445
LO.454253
LO.5314
LO.6535
LO.74452
LO.8444542

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

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