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Nonlinear Dynamics in Complex Networks

Wahllehrveranstaltung 3233 L 507 im Sommersemester 2019

Dozent: Dr. Anna Zakharova,

Vorlesung:

Di 10:15-11:45 EW 733 (Beginn 09.04.2019)

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.

Außerdem gibt es in diesem Semester ein ergänzendes Seminar zum Thema "Nonlinear Dynamics of Adaptive Networks".

Inhalt

The lectures cover the main concepts of nonlinear dynamics, emphasizing characterization of complex networks. First, the basic ideas of nonlinear dynamics, such as description of nonlinear systems, stability analysis, bifurcations and attractors will be introduced. Further, the main concepts of the theory of complex networks will be explained. A special attention will be paid to synchronization phenomena including partial synchronization patterns. Synchronization is 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. Various applications in different fields of science including physics, chemistry, biology and engineering will be discussed.

Literatur

Books:

  • S. Strogatz, Nonlinear Dynamics and Chaos: With Applications To Physics Biology, Chemistry And Engineering, Westview Press (2000)
  • S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Complex networks: Structure and dynamics, Phys. Rep. 424, 4-5, 175 (2006).
  • A. Zakharova, Chimera Patterns in Networks: Interplay between Dynamics, Structure, Noise, and Delay, Series: Understanding Complex Systems, Springer (2019)
  • 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)
  • V. S. Anishchenko, T. Vadivasova and G. Strelkova, Deterministic Nonlinear Systems, Springer Series in Synergetics, Springer (2014)
  • S. Boccaletti, A. N. Pisarchik, C. I. del Genio and A. Amann, Synchronization: From Coupled Systems to Complex Networks, Cambridge University Press (2018)

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