Lecturer: Dr. Sajjad Bakrani and Çelik Özdeş

This course was 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 was provided in this course. To give deep understanding of concepts, lots of examples and numerical simulations were presented in the course.

Topics covered: Basics of ODEs, Linear systems, Stability of equilibria and periodic orbits, Lyapunov functions, Chaos theory (Lyapunov exponents, strange attractors, etc.), Basic algebraic graph theory (Laplacian matrices and their spectra), Complete synchronization in coupled systems.