Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn


Speaker: Philipp Hoevel, Institut für Theoretische Physik, TU Berlin, and Nonlinear Dynamics and Control in Neuroscience, Bernstein Center for Computational Neuroscience Berlin

Title: Synchronization in networks with delay * Colloquium on Complex and Biological Systems

Time: Fri, July 5, 2013, 10:15am

Place: bldg 28, room 0.108

The field of nonlinear dynamics in coupled systems has seen a huge increase in interest during the last years. The size of considered systems ranges from a few coupled elements to complex networks, and collective dynamics may arise in various patterns, of which in-phase (or zero-lag) synchronization is the most prominent. Traveling waves and cluster or group synchronization are other examples. In particular, during cluster synchronization, parts of a network synchronize with zero lag, but with a nonzero phase-lag between different clusters. The signal transmission between coupled elements is often not instantaneous. Thus non-zero transmission times have to be taken into account as crucial quantities that influence the dynamics of network nodes to a large extent.
In this presentation, I will discuss synchronization effects in the presence of delayed coupling for neural systems. I will show that already two coupled oscillators give rise to intricate scenarios, especially for asymmetric delays in the mutual and self-coupling [1]. In addition, I will also consider the case of networks of coupled elements, where I use the method of the Master Stability Function to investigate the stability of the zero-lag synchronized dynamics of the network nodes [2]. One important implication of my results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronization, but may also restabilize synchronization or introduce multiple transitions between synchronization and desynchronization [3].
[1] A. Panchuk, D. P. Rosin, P. Hövel, and E. Schöll: Synchronization of coupled neural oscillators with heterogeneous delays Int. J. Bif. Chaos (2013), in print. Available as: arXiv:1206.0789.
[2] A. Keane, T. Dahms, J. Lehnert, S. A. Suryanarayana, P. Hövel, and E. Schöll: Synchronisation in networks of delay-coupled type-I excitable systems Eur. Phys. J. B 85, 407 (2012).
[3] J. Lehnert, T. Dahms, P. Hövel, and E. Schöll: Loss of synchronization in complex neural networks with delay Europhys. Lett. 96, 60013 (2011).

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Udo Schwarz, Zentrum für Dynamik komplexer Systeme,
Universität Potsdam, Campus Golm Karl-Liebknecht-Str. 24, 14476 Potsdam, building 28, room 2.107
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