A stochastic version of the Jansen and Rit neural mass model: Analysis and numerics

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.