Dresden 2006 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 15: Quantum Chaos

DY 15.2: Vortrag

Montag, 27. März 2006, 15:15–15:30, SCH 251

From irregular subthreshold oscillations to intermittent spiking: canard explosion for a chaotic attractor — •Michael Zaks, Xaver Sailer , and Lutz Schimansky-Geier — Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin

In a deterministic model of a neuron with one fast and two slow variables, we observe the crisis of a chaotic attractor: a minute parameter variation causes the strong abrupt (albeit continuous) increase of the amplitude of irregular oscillations. In contrast to conventional types of attractor crises, this phenomenon owes to separation of characteristic timescales; it is related to the motion of the system in the phase space along the repelling part of the slow surface. In contrast to the conventional canard explosion, the transition is experienced not by a single limit cycle but by the attracting chaotic set. For the discussed model the crisis marks the transition from the state of chaotic subthreshold oscillations to the regime of intermittent chaotic spiking. Similar phenomena have been recovered in collective dynamics of large ensembles of globally coupled slow-fast stochastic oscillators.