Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Tuesday, 08.05.2012 17 c.t.

Emergent dynamics of coupled oscillators

by Prof. Dr. Yuri Maistrenko
from Universität Potsdam

Contact person: Marc Timme


Ludwig Prandtl lecture hall


Phase-coupled oscillators serve as paradigmatic models of dynamical networks in physics, biology other fields. Even if the oscillators are identical and the coupling scheme is symmetric they can demonstrate surprising variety of complex collective behaviors - from phase and frequency clustering to developed space-temporal chaos. A characteristic example is given by chimera states for non-globally coupled Kuramoto-Sakaguchi model. The other examples are obtained when varying the coupling topology and its shape. We analyze a two-group network of globally coupled phase oscillators including attractive and repulsive interactions as prototypes of excitatory and inhibitory connections in neuronal networks. If excitation is stronger, the network dynamics tend to ensure complete synchronization. In the opposite case, i.e. when inhibition is predominant, highly asymmetric phase clusters arise in which one or more oscillators split up from the others synchronized. A special interest is offered by a solitary state where the only one splitting oscillator stays in anti-phase to the major cluster. We find analytically parameter regions for stability of the solitary and other clustered states and show that they typically arise in more general networks of this structure, e.g. Va der Pol, Stuardt-Landau, FitzHug-Nagumo.

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