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Bifurcation Analysis of Jansen's Neural Mass Model

Francois.Grimbert{at}sophia.inria.fr

Olivier Faugeras

Olivier.Faugeras{at}sophia.inria.fr Odyssée Laboratory, INRIA/ENPC/ENS, INRIA Sophia-Antipolis, 06902 Sophia Antipolis, France.

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.