Theory of Neural Synchrony

GERMAN MATO

Methods and Models in Neurophysics

Elsevier

Lugar: Amsterdam; Año: 2004; p. 125 - 178

The nervous system controls the behavior of the organism by going through a different number of dynamical states. In some cases the dynamical states have a functional role, such as the synchronized oscillations responsible for the respiratory rhythms, in other cases they are pathological, such as the oscillations observed during the Parkinson disease or their role can be unknown, as in the different oscillations observed during sleep. In this context one objective is tounderstand which features of the network are relevant to control the dynamics and, if possible, to find some rule that would allow us to predict the effect of some change in the parameters. The dynamics of the network is controlled by a complex systemof non-linear equations. One possible approach to the understanding of the collective dynamics is to use extensive numerical simulations to explore the space of parameters. This has the obvious drawback that an exhaustive search is clearly impossible. Moreover, as the various parameters interact in a complex non-linear way, it would be very difficult to extract from simulations general conclusions and predictions about the global behavior. For these reasons, approximate analytical or semi-analytical methods have been introduced. These methods consider some special cases that allow to simplify considerably the dynamics of the network and to draw general conclusions about which are the more relevant parameters. Subsequently these results can be extended to more realistic situations by performing numerical simulations.