A stochastic version of the Jansen and Rit neural mass model: Analysis and numerics
Sprache des Titels:
Neural mass models provide a useful framework for modelling mesoscopic neural
dynamics and in this article we consider the Jansen and Rit neural mass model (JR-NMM).
We formulate a stochastic version of it which arises by incorporating random input and has
the structure of a damped stochastic Hamiltonian system with nonlinear displacement. We
then investigate path properties and moment bounds of the model. Moreover, we study the
asymptotic behaviour of the model and provide long-time stability results by establishing the
geometric ergodicity of the system, which means that the system?independently of the
initial values?always converges to an invariant measure. In the last part, we simulate the
stochastic JR-NMM by an efficient numerical scheme based on a splitting approach which
preserves the qualitative behaviour of the solution.