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Updated: Jul 19, 2026

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
Published on: June 21, 2022
Bifurcation analysis of Jansen's neural mass model
François Grimbert1, Olivier Faugeras
1Francois.Grimbert@sophia.inria.fr
Abstract:
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.
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