Mean field models (MFMs) of cortical tissue incorporate salient features of
neural masses to model activity at the population level. One of the common
aspects of MFM descriptions is the presence of a high dimensional parameter
space capturing neurobiological attributes relevant to brain dynamics. We study
the physiological parameter space of a MFM of electrocortical activity and
discover robust correlations between physiological attributes of the model
cortex and its dynamical features. These correlations are revealed by the study
of bifurcation plots, which show that the model responses to changes in
inhibition belong to two families. After investigating and characterizing
these, we discuss their essential differences in terms of four important
aspects: power responses with respect to the modeled action of anesthetics,
reaction to exogenous stimuli, distribution of model parameters and oscillatory
repertoires when inhibition is enhanced. Furthermore, while the complexity of
sustained periodic orbits differs significantly between families, we are able
to show how metamorphoses between the families can be brought about by
exogenous stimuli. We unveil links between measurable physiological attributes
of the brain and dynamical patterns that are not accessible by linear methods.
They emerge when the parameter space is partitioned according to bifurcation
responses. This partitioning cannot be achieved by the investigation of only a
small number of parameter sets, but is the result of an automated bifurcation
analysis of a representative sample of 73,454 physiologically admissible sets.
Our approach generalizes straightforwardly and is well suited to probing the
dynamics of other models with large and complex parameter spaces