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A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation

Fig 2

Two-dimensional bifurcation analysis.

Here, we illustrate the bifurcation diagram of the isolated thalamus with respect to the two key parameters and . The interaction between the currents incorporated into the thalamic module results in the emergence of two torus bifurcations via a blue sky catastrophe. They lead to spindle oscillations in the orange shaded regions. The left spindle regime (S_I) is encased by a Hopf and a torus bifurcation, whereas the right spindle regime (S_II) is constrained by two global bifurcations that are indicated by the dashed gray lines. The vertical line marks the emergence of the torus bifurcation, whereas the horizontal gray line marks the cusp bifurcation where the two saddle-nodes that accompany the left torus bifurcation vanish. The torus bifurcation on the right marks the transition from spindle oscillations to delta oscillations. The labeled points mark the parameter settings utilized in Fig 3, which are given in Table 1.

doi: https://doi.org/10.1371/journal.pcbi.1005022.g002