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Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - International Research Training Group 1740

Project 01



Evolution from small to large networks, their spectrum and related bifurcation scenarios



About the project:

Real world systems can be considered as networks consisting of many interacting elements. Recent studies show that the network structure can have dramatic influences on the dynamical properties of complex systems. This project deals with the dynamics of complex networks.


Goals:

  • Study of the dynamical properties of networks, which are obtained by adding new connections to a regular lattice
  • Investigation of composed networks, where few of the regular sub-networks are coupled
  • Discovering the bifurcation scenarios in the above mentioned systems
  • Applications of the results to the networks used in climate modeling, as well as to neuronal models


Members:

  • PD Dr.sc. Serhiy Yanchuk
    Head of the junior research group for Applied Mathematics, Institute of Mathematics, Humboldt University of Berlin.
  • Jan Philipp Pade
    PhD student in mathematics. I studied mathematics at the „Freie Universität Berlin“ and graduated with a Diploma under supervision of Dr. K. Matthies. Thereafter I've been working in the field of neuroscience for three years.

Recent related publications:

  • O. Popovych, S. Yanchuk and P. Tass: Delay- and coupling-induced firing patterns in oscillatory neural loops, Phys. Rev. Lett. 107, 228102 (2011), PDF
  • S. Heiligenthal, Th. Dahms, S. Yanchuk, Th. Jüngling, V. Flunkert, I. Kanter, E. Schöll, W. Kinzel: Strong and weak chaos in nonlinear networks with time-delayed couplings, Phys. Rev. Lett. 107, 234102 (2011)
  • V. Flunkert, S. Yanchuk, T. Dahms, E. Schöll: Synchronizing distant nodes: a universal classification of networks, Phys. Rev. Lett. 105, 254101 (2010)
  • P. Perlikowski, S. Yanchuk, M. Wolfrum, A. Stefanski, P. Mosiolek and T. Kapitaniak: Routes to complex dynamics in a ring of unidirectionally coupled systems, Chaos, 20, 013111 (2010)