Local excitation solutions in one-dimensional neural fields by external input stimuli

Cortical neurons are massively connected with other cortical and subcortical cells, and they receive synaptic inputs from multiple sources. To explore the basis of how interconnected cortical cells are locally activated by such inputs, we theoretically analyze the local excitation patterns elicited by external input stimuli by using a one-dimensional neural field model. We examine the conditions for the existence and stability of the local excitation solutions under arbitrary time-invariant inputs and establish a graphic analysis method that can detect all steady local excitation solutions and examine their stability. We apply this method to a case where a pair of supra- and subthreshold stimuli are applied to nearby positions in the field. The results demonstrate that there can exist bistable local excitation solutions with different lengths and that the local excitation exhibits hysteretic behavior when the relative distance between the two stimuli is altered.

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