Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 81: Nonlinear Dynamics, Synchronization, Chaos II

DY 81.4: Vortrag

Freitag, 16. März 2018, 10:45–11:00, BH-N 243

Dynamics in ensembles of excitable units with global repulsive coupling — •Michael Zaks — Humboldt Universität zu Berlin, Institut für Physik

We consider ensembles build from excitable elements. In contrast to oscillators, isolated excitable units feature no oscillatory dynamics but stay at rest. Excitability means that for finite-size disturbances relaxation to the equilibrium is preceded by a large-scale excursion in the phase space. Description of this property, shared e.g. by many cortical cells, can be reduced to dynamics on the circle: the so-called "active rotator". Attractive coupling draws together an ensemble of excitable elements: stability of the equilibrium is enhanced. In contrast, repulsive coupling (an example is delivered by inhibitory neurons), weakens stability. Under sufficiently strong repulsion the equilibrium gets destabilized, and the large-scale oscillations commence: the formerly quiescent system acquires dynamics that completely owes to the interactions. For an ensemble of identical active rotators with global repulsive coupling the onset of oscillations occurs via the global event: the transcritical heteroclinic bifurcation. The number of unstable states of equilibrium, involved in the bifurcation, exponentially grows with the size of the ensemble. This transition gives rise to a large amount of stable periodic motions; moreover, if the coupling to the global field is restricted to the first Fourier harmonics of the rotator phase, the Strogatz-Watanabe phenomenon takes place, and the attracting periodic states fill high-dimensional continua. We discuss collective oscillations both for small ensemble of excitable units and in the thermodynamical limit.