Dynamical Systems in Neuroscience:

124 Two-Dimensional Systemsexcitation blocksupercriticalAndronov-Hopfbifurcation20 mV100 ms-60 mVinjected current-10 mV180 pAFigure 4.36: Excitation block in layer 5 pyramidal neuron of rat’s visual cortex as theamplitude of the injected current ramps up.Supercritical and subcritical Andronov-Hopf bifurcations in neurons result in slightlydifferent neuro-computational properties. In contrast, the saddle-node and Andronov-Hopf bifurcations result in dramatically different neuro-computational properties. Inparticular, neurons near saddle-node bifurcation act as integrators — they prefer highfrequencyinput: The higher the frequency of the input, the sooner they fire. Incontrast, neural systems near Andronov-Hopf bifurcation have damped oscillatory potentialsand they act as resonators — they prefer oscillatory input with the samefrequency as that of damped oscillations. Increasing the frequency may delay or eventerminate their response. We discuss this and other neuro-computational properties inChap. 7.