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Synchronization from mathematical point of view

  • Level: Advanced
  • Status: Upcoming
  • Offered by: Kadir Has University
  • Poster

Course Form

Academic Institution offering the course Kadir Has University
Mode of Delivery
(in class / online / blended)
Online
Prerequisites by topic Calculus, Differential Equations, Basic Linear Algebra
Language of Instruction English
Course Coordinator Deniz Eroglu
Course Lecturer(s) Sajjad Bakrani, Celik Ozdes
Course Assistant(s) Celik Ozdes
Course Objectives This course is an introduction to synchronization phenomenon in complex systems from mathematical point of view. The required mathematical theory (in particular, dynamical systems theory) for understanding synchronization in networks will be provided in this course. To give deep understanding of concepts, lots of examples and numerical simulations will be presented in the course.
Course Contents 1. Collective dynamics through examples
2. Theory of ODEs (basic concepts, linear systems, stability, chaos, bifurcations)
3. Synchronization
4. Numerics and programming
Learning Outcomes of the Course Unit 1. Gaining the mathematical (rigorous and numerical) background to understand synchronization in network.
2. Computational understanding of differential equations.Lectures and practice sessions, numerical simulations, animations and exercises for self-assessment
Planned Learning Activities and Teaching Methods Lectures and practice sessions, numerical simulations, animations and exercises for self-assessment
Recommended or Required Reading • Deniz Eroglu, Jeroen S.W. Lamb, Tiago Pereira, “Synchronisation of chaos and its applications”, Contemporary Physics, 2017
• Sebastian Van Strien, “Lecture notes on Differential Equations”, wwwf.imperial.ac.uk/~svanstri/Files/de-4th.pdf
Other Course Resources Morris W. Hirsch, Stephen Smale, Robert L. Devaney, “Differential equations, dynamical systems, and an introduction to chaos”, Academic press, 2012.


WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES


Week Subjects
1 An introduction to collective dynamics
2 Dynamical systems in nutshell
3 Basic theory of ODEs - Part 1
4 Basic theory of ODEs - Part 2
5 Linear Systems
6 Stability theory
7 Dissipative systems
8 Bifurcations
9 Chaotic dynamics
10 Synchronization of chaos
11 Hands-on programming: session 1
12 Hands-on programming: session 2

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