A stochastic version of a neural mass model - properties and numerics
Sprache des Vortragstitels:
2nd International Conference on Mathematical NeuroScience (ICMNS)
Sprache des Tagungstitel:
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 variance of the solution, 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.