Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Ann-Katrin Becher
Universität zu Köln
Phase Synchronization in a network of inhibitory and excitatory coupled oscillators
The phenomenon of phase synchronization plays a crucial role in many systems of biology, physics and
neurosciences which can be modelled by phase coupled oscillators. One popular model that exhibits
phase synchronization is the Kuramoto system.
In this talk a similar model of phase coupled oscillators is introduced describing a network with both
excitatory and inhibitory interactions. The phase dynamics are modelled by a Kuramoto-like system
without symmetries with regard to coupling. The coexistence of inhibitory and excitatory interactions and
the asymmetry of coupling give rise to several different scenarios of synchronization. Excitatory coupling
can result in “in phase” oscillations. In contrast inhibitory coupled oscillators tend to oscillate “anti-phase”.
Therefore a combination of both types of coupling can lead to transitional states or coexistence of stable
in phase and anti-phase oscillations. In the talk the phase model is introduced and some of the results
concerning the excitatory-inhibitory-synchronization behavior are presented.
Sevda Ça ˘gırıcı
Mathematical Institute, University of Cologne
Amplitude Dynamics in the Model of Two Nonlinear Coupled Oscillators
We analyse a system of two nonlinear coupled oscillators describing amplitude and phase dynamics,
which can be seen as a four dimensional model of two neurons. The major point of our investigations is to
study the influence of the inhibitory synaptic coupling between neurons upon the amplitude dynamics. In
addition we show some results of our model with external stimulus which corresponding to real EEG-Data
from auditory processing in shizophrenia.
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