Regensburg 2016 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 37: Nonlinear Dynamics, Synchronization and Chaos
DY 37.5: Vortrag
Mittwoch, 9. März 2016, 11:00–11:15, H48
Eigenmode decomposition for synchronized solutions in networks with heterogeneous delay coupling — •Andreas Otto1, Gabor Orosz2, Daniel Bachrathy3, and Günter Radons1 — 1Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany — 2Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA — 3Department of Applied Mechanics, Budapest University of Technology and Economics , H1111, Budapest, Hungary
Synchronization in networks of delay-coupled nonlinear systems can be found, for example, in social systems, biology, engineering or physics. In technical applications, e.g. in coupled semiconductor lasers, the time-delays can be tuned to be identical, whereas in real world systems, such as neuronal or social networks, the delays are typically heterogeneous. For networks with instantaneous or identical delays the master stability function can be used to analyze the stability of the network eigenmodes. For heterogeneous delays this approach is restricted to the specific case, where the coupling matrices for the different delays commute. A general approach for the decomposition of the network eigenmodes around synchronized equilibria has been proposed in [1]. In this talk, an extension of this general approach for the eigenmode decomposition around synchronized periodic orbits is presented. In this case the master stability function becomes, in general, a periodic delay differential equation with multiple delays. Numerical results on the stability are shown for delay-coupled Hodgkin-Huxley neurons.
[1] R. Szalai and G. Orosz, Phys. Rev. E 88, 040902 (2013).