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CoursesNonlinear Dynamics in Complex Systems and Networks

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Important Information

The lectures will take place online via a video conferencing tool.

To enter the lecture room, follow this link: 


The first lecture will take place on April 22 at 10:15.

Please register in ISIS to access the digital material.

Nonlinear Dynamics in Complex Systems and Networks

Wahllehrveranstaltung 3233 L 521 im Sommersemester 2020

Lecturer: Prof. Dr. Anna Zakharova,


We 10:15-11:45 EW 733 (first lecture on 22.04.2020)

SAP number 3233 L 521

When attending this course 3 credit points within the ECTS system can be obtained. In combination with the Tutorial (SAP number 3233 L 522) 6 credit points can be obtained. More information on the "Modul -Spezielle Themen der Theoretischen Physik" can be found here:


The course is suitable for students of physics (MSc), mathematics (MSc) and other natural science MSc programmes and interested members of the SFB 910. 

The course will be given in English.

The following courses in Summer Term 2020 are recommended:

- Tutorial "Nonlinear Dynamics in Complex Systems and Networks": LV-Nr. 3233 L 522, Wednesdays 16:15 -17:45 via Zoom (link in ISIS announcement "Tutorial - New Time")

- Seminar "Multilayer Networks: Applications and Related Concepts": LV-Nr. 3233 L 611, Tuesday 16:15, via Zoom


The lectures cover the main concepts of nonlinear dynamics. First, the basic ideas of nonlinear dynamics, such as the description of nonlinear systems, stability analysis, bifurcations, and attractors will be introduced. Further, we will discuss the main concepts of the synchronization theory and apply the tools of nonlinear dynamics to analyze synchronization phenomena. Special attention will be paid to partial synchronization patterns. Synchronization is one of the fundamental phenomena in nature. Fireflies flashing in unison, the 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 stochastic systems, from two coupled units to complex networks. Various applications in different fields of science including physics, chemistry, biology, and engineering will be discussed.



  • A. Zakharova, Chimera Patterns in Networks: Interplay between Dynamics, Structure, Noise, and Delay, Series: Understanding Complex Systems, Springer (2020)
  • S. Boccaletti, A. N. Pisarchik, C. I. del Genio and A. Amann, Synchronization: From Coupled Systems to Complex Networks, Cambridge University Press (2018)
  • V. S. Anishchenko, T. Vadivasova and G. Strelkova, Deterministic Nonlinear Systems, Springer Series in Synergetics, Springer (2014)
  • S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Complex networks: Structure and dynamics, Phys. Rep. 424, 4-5, 175 (2006)
  • S. Strogatz, Sync: The Emerging Science of Spontaneous Order, Hyperion Press, New York (2003)
  • A. Pikovsky, M.G. Rosenblum and J. Kurths, Synchronization: a universal concept in nonlinear sciences, Cambridge University Press (2001)
  • S. Strogatz, Nonlinear Dynamics and Chaos: With Applications To Physics Biology, Chemistry And Engineering, Westview Press (2000)
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