2006/10/19 by François Grimbert, Olivier Faugeras · 3 citations
Neuroscience · Physics and Astronomy · #Neural dynamics and brain function #Neuroscience and Neuropharmacology Research #stochastic dynamics and bifurcation
paper · doi:10.1162/neco.2006.18.12.3052
openalex publication_date 2006/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We present a mathematical model of a neural mass developed by a number of people, including Lopes da Silva and Jansen. This model features three interacting populations of cortical neurons and is described by a six-dimensional nonlinear dynamical system. We address some aspects of its behavior through a bifurcation analysis with respect to the input parameter of the system. This leads to a compact description of the oscillatory behaviors observed in Jansen and Rit (1995) (alpha activity) and Wendling, Bellanger, Bartolomei, and Chauvel (2000) (spike-like epileptic activity). In the case of small or slow variation of the input, the model can even be described as a binary unit. Again using the bifurcation framework, we discuss the influence of other parameters of the system on the behavior of the neural mass model.