Towards dynamical system models of language-related brain potentials

Abstract

Event-related brain potentials (ERP) are important neural correlates of cognitive processes. In the domain of language processing, the N400 and P600 reflect lexical-semantic integration and syntactic processing problems, respectively. We suggest an interpretation of these markers in terms of dynamical system theory and present two nonlinear dynamical models for syntactic computations where different processing strategies correspond to functionally different regions in the system's phase space.

Fig. 1

GB phrase structure trees. (a) For the sentence (33). (b) For the sentence (34)

Fig. 2

Event-related brain potentials for the (blue) and (red) sentences ((33 and 34), respectively) at the parieto-central electrode Pz. (a) ERP voltage averages. (b) Event-related cylinder entropies obtained from a half-wave symbolic encoding with parameters T₁ = 70ms, T₂ = 10ms, and l = 8ms. Waveforms are digitally low-pass filtered with a cut-off frequency of 10Hz for better visibility. The disambiguating words der versus den appeared at t₀ = 0s. Language-related ERPs, N400 and P600, are indicated by arrows

Fig. 3

Return plot of the first principal component, PC#1, of the tensor product top-down recognizer processing the (blue) and (red) sentences (33 and 34), respectively

Fig. 4

Time series of the first principal component of the tensor product top-down recognizer in phase space processing the (blue) and (red) sentences (33 and 34), respectively. The model “P600” is indicated by the arrow

Fig. 5

Phase space dynamics of input-driven nonlinear automaton processing the sentence (33). Each layer displays one iteration of the NDA top-down recognizer. The initial condition is indicated by “*”; non-autonomous operations are indicated by “°”

Fig. 6

Phase space dynamics of input-driven nonlinear automaton processing the sentence (34). Here, only one non-autonomous operation is indicated by “°”. The diagnosis and repair transitions are indicated by “*”. (a) Global view. (b) Enlargement

Fig. 7

Measurement partition of the NDA phase space. Grid density is shown logarithmically

Fig. 8

Time series of the cylinder entropy of the NDA top-down recognizer processing the (blue) and (red) sentences (33 and 34), respectively. The model “N400’s and the “P600” are indicated by arrows