A Stochastic Version of a Neural Mass Model - Analysis and Numerics
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
5th Austrian Stochastics Days
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
Neural mass models provide a useful framework for modelling mesoscopic neural dynamics and in this talk we consider the Jansen and Rit Neural Mass Model (JR-NMM). This system of ODEs has been introduced as a model in the context of electroencephalography (EEG) rhythms and evoked potentials and has been proposed as an underlying model in various application settings. Incorporating random input, we formulate a stochastic version of the JR-NMM which has the structure of a nonlinear stochastic oscillator. We introduce the stochastic analogon of the convolution-based formulation of the JR-NMM and derive several properties of the stochastic system, e.g. estimates on the expected value and the second moment of the solution, bounds on the escape probability and long-term behaviour of the solution. Finally, we briefly address the question of efficient numerical integrators based on a splitting approach which preserve the qualitative behaviour of the solution.
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