Synchronization and Chimera States in Complex Networks

Wahllehrveranstaltung 3233 L 507 im Wintersemester 2017/18

Dozent: Dr. Anna Zakharova, anna.zakharova@tu-berlin.de

Vorlesung:
Mi 10:15-11:45 EW 733 (Beginn 18.10.)

Für Studierende der Physik (Master), Mathematik (Master) und anderer naturwissenschaftlicher Masterstudiengänge und interessierte Mitglieder des SFB 910.

When attending this course 3 credit points within the ECTS system can be obtained. The course will be given in English.

Zusammen mit der Lehrveranstaltung LV 3232 L 120 „Theoretische Physik VI (Vertiefung): Nichtlineare Dynamik und Kontrolle"(zuletzt gelesen im SS 2016)  kann diese Vorlesung auch zu einem physikalischen Wahlpflichtmodul (8 SWS)  mit 12 ECTS kombiniert werden.

Außerdem gibt es in diesem Semester ein ergänzendes Seminar zum Thema "Nonlinear Dynamics of Complex Neural Systems".

The lectures cover the main concepts of synchronization - one of the fundamental phenomena in nature. Fireflies flashing in unison, coordinated firing of pacemaker cells in our hearts, fish swimming in a synchronized swarm – these are just a few real-world examples of self-organization. We will discuss synchronization in various systems ranging from periodic oscillators to chaotic and stochastic systems, from two coupled units to complex networks. A special attention will be paid to a peculiar type of partial synchronization pattern, chimera states. Discovered very recently, these hybrid states are made up of spatially separated domains of synchronized and desynchronized behavior. They arise surprisingly in networks of completely identical units and symmetric coupling topologies. These intriguing patterns are named after a fabulous fire-breathing creature from Greek mythology that has a lion's, a goat's, and a snake's head. As the counter intuitive dynamical state, this monster is also composed of incongruous parts. Various applications in different fields of science including physics, chemistry, biology and engineering will be presented. More specifically, the following topics will be discussed in the lectures:

 

• synchronization of periodic oscillators

• synchronization of two and many oscillators

• synchronization of chaotic systems

• synchronization in the presence of noise

• coherence resonance

• synchronization in complex networks

• partial synchronization patterns

• transition from synchronization to desynchronization

• chimera states

• impact of noise and delay on chimera states

18.10. Introduction: Sync, https://www.ted.com/talks/steven_strogatz_on_sync

25.10. What is sync? Classical example of a pendulum clock

01.11. Synchronization of periodic oscillators by periodic external action

15.11. Lecture 5

Books:

• S. Strogatz, Nonlinear Dynamics and Chaos: With Applications To Physics Biology, Chemistry And Engineering, Westview Press (2000)
• Anishchenko, V. S., Astakhov, V., Neiman, A. B., Vadivasova, T. and Schimansky-Geier, L., Nonlinear dynamics of chaotic and stochastic systems: tutorial and modern developments, Springer (2007).
• S. Strogatz, Sync: The Emerging Science of Spontaneous Order, Hyperion Press, New York (2003).