Title |
A Stochastic Version of the Jansen and Rit Neural Mass Model: Analysis and Numerics
|
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Published in |
The Journal of Mathematical Neuroscience, August 2017
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DOI | 10.1186/s13408-017-0046-4 |
Pubmed ID | |
Authors |
Markus Ableidinger, Evelyn Buckwar, Harald Hinterleitner |
Abstract |
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. |
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