Reference : Existence and stability of limit cycles in a macroscopic neuronal population model
Scientific journals : Article
Life sciences : Multidisciplinary, general & others
http://hdl.handle.net/10993/20318
Existence and stability of limit cycles in a macroscopic neuronal population model
English
Rodrigues, Sandra mailto [University of Luxembourg > Central Administration > Finance and Accounting Department]
Goncalves, Jorge mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Terry, J. mailto [> >]
Sep-2007
Physica D: Nonlinear Phenomena
233
1
39-65
Yes (verified by ORBilu)
0167-2789
[en] Human EEG ; Mathematical modelling ; Macroscopic population model ; Normal forms ; Global stability ; Limit cycle oscillations ; Epilepsy
[en] We present rigorous results concerning the existence and stability of limit cycles in a macroscopic model of neuronal activity. The specific model we consider is developed from the Ki set methodology, popularized by Walter Freeman. In particular we focus on a specific reduction of the KII sets, denoted RKII sets. We analyse the unfolding of supercritical Hopf bifurcations via consideration of the normal forms and centre manifold reductions. Subsequently we analyse the global stability of limit cycles on a region of parameter space and this is achieved by applying a new methodology termed Global Analysis of Piecewise Linear Systems. The analysis presented may also be used to consider coupled systems of this type. A number of macroscopic mean-field approaches to modelling human EEG may be considered as coupled RKII networks. Hence developing a theoretical understanding of the onset of oscillations in models of this type has important implications in clinical neuroscience, as limit cycle oscillations have been demonstrated to be critical in the onset of certain types of epilepsy.
http://hdl.handle.net/10993/20318
10.1016/j.physd.2007.06.010

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