Research on Hopf bifurcation of cortical column model with time delay

Electroencephalogram (EEG) model is an expression of cortical neural electrical activity, and it helps us to recognize brain electrophysiological process. Considering time delay between excitatory and inhibitory neurons during information transformation, this paper studies the effect of time delay on a class of lumped parameter cortical column model. The stability of equilibrium point is analyzed, and the condition for Hopf bifurcation is achieved. Numerical simulation shows that the model can generate several kinds of EEG-like waveforms and rhythms under different parameters. The simulation verifies the effectiveness of mathematical results. The study on bifurcation of EEG provides more evidence for brain´s nonlinear structure.