A stochastic version of the jansen and rit neural mass model: analysis and numerics

DOI10.1186/s13408-017-0046-4zbMath1395.92027OpenAlexW2744593609WikidataQ41489143 ScholiaQ41489143MaRDI QIDQ723672

Evelyn Buckwar, Markus Ableidinger, Harald Hinterleitner

Publication date: 24 July 2018

Published in: The Journal of Mathematical Neuroscience (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13408-017-0046-4

zbMATH Keywords

asymptotic behaviourstochastic Hamiltonian systemJansen and Rit neural mass modelstochastic splitting schemes

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Neural biology (92C20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Asymptotic properties of solutions to ordinary differential equations (34D05)

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A splitting method for SDEs with locally Lipschitz drift: illustration on the FitzHugh-Nagumo model ⋮ General order conditions for stochastic partitioned Runge-Kutta methods ⋮ Diffusion approximation of multi-class Hawkes processes: Theoretical and numerical analysis ⋮ Parametric inference for hypoelliptic ergodic diffusions with full observations ⋮ Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs ⋮ Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motion ⋮ Density estimates and short-time asymptotics for a hypoelliptic diffusion process ⋮ A new class of structure-preserving stochastic exponential Runge-Kutta integrators for stochastic differential equations

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