Bifurcations in neural masses
Résumé
Neural continuum networks are an important aspect of the modeling of macroscopic parts of the cortex. They have been first studied by Amari[6]. These networks have then been the basis to model the visual cortex by Bresslov[4]. From a computational viewpoint, the neural masses could be used to perform image processing like segmentation, contour detection... The neural masses model is also well suited to study the impact of the delays in the dynamics of neural networks, for example see Roxin [8]. Thus, there is a need to develop tools (theoretical and numerical) allowing the study of the dynamical and stationary properties of the neural masses equations. In this paper, we look at the dependency of neural masses stationary solutions with respect to the stiffness of the nonlinearity. This is done by using bifurcation theory in infinite dimensions. We provide a useful approximation of the connectivity matrix and give numerical examples of bifurcated branches which had not been yet fully computed in the literature. The analysis relies on the study of a simple model thought generic in the sense it has the properties that any neural mass system should possess generically.
Origine : Accord explicite pour ce dépôt
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