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Seminar: Self-Organization in Complex Nonlinear Systems

Location: EW 731 (PN 731)

Time: Thursday, 25.10.2007, 16:15

Suppression of synchronized oscillations: Noise-, variability-, and delay-induced transition in a net of FitzHugh-Nagumo elements

Martin Gassel (TU Darmstadt)

Neural systems show a great variety of different dynamics, which often can be
characterized as excitable or oscillatory behavior. Synchronized oscillations
of an ensemble of neural elements are not always desirable, because this
regular activity is believed to play a crucial role in the emergence of
pathological rhythmic brain activity in Parkinson's disease, essential tremor
and epilepsy. The presented studies focus on the transition from global
synchronized oscillations to excitable dynamics in a net of FitzHugh-Nagumo
elements. This transition from global oscillation to excitability can be
induced by multiplicative noise. The systematic influence of multiplicative
noise, which leads to the stabilization of the former unstable focus, can be
explained using the small noise expansion. In a very similar way
multiplicative variability (static stochastic differences between the
otherwise equal elements of the net) can induce the transition to
excitability. Another method to suppress the global oscillation and to induce
excitable dynamics is to apply time-delayed feedback. For an appropriate
chosen feedback strength and delay time the former unstable focus becomes
stabilized, which can be predicted very well by a linear stability analysis.
So via noise, variability and time-delayed feedback the global oscillation
can be suppressed and the possibility of signal transmission through the net
(excitation waves) can be induced.

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