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The present work derives the spatiotemporal field equation of neural populations considering two types of neurons. The model considers pyramidal cells, which may excite or inhibit other neurons, and GABAergic interneurons inhibiting terminal neurons. Additionally, taking into account excitatory and inhibitory synapses, the neural population obeys a vector-field equation involving nonlocal spatial interactions. The work studies the effect of the anesthetic agent propofol, which increases the decay time of inhibitory synapses. In addition, it explains the bifurcation mechanism in some detail and finds a saddle-node bifurcation subject to the propofol concentration. This bifurcation may model the transition between consciousness and nonconsciousness and vice versa during the administration of general anesthetics in medicine.

Anesthetic-Induced Transitions by Propofol Modeled by Nonlocal Neural Populations Involving Two Neuron Types