The corticothalamic Compact Model with time delay proposed by Kim and Robinson is successfully reduced to a real Ginzburg-Landau equation in the vicinity of pitchfork bifurcation point, using center manifold theory for functional differential equations and perturbation theory of week interactions. Broad agreement between the predictions with the reduced equation and corresponding numerical results with the original equation are confirmed in transient analysis of single-body and two-body problem, with emphasis that a “projection to the center subspace” is essential. Furthermore, analogies with Ginzburg-Landau theory of phase transition and with theory developed by Benayoun et al. of neural avalanches are pointed out.
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