Bifurcation analysis of Jansen's neural mass model.
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.
Grimbert
François
F
Francois.Grimbert@sophia.inria.fr
Faugeras
Olivier
O
D000200:Action Potentials / Q000502:physiology; D000513:Alpha Rhythm; D000818:Animals; D003198:Computer Simulation; D004827:Epilepsy / Q000503:physiopathology; D008959:Models, Neurological; D009474:Neurons / Q000145:classification / Q000502:physiology*; D017711:Nonlinear Dynamics