Dynamical Systems in Neuroscience:

Two-Dimensional Systems 121-20-50-30sa dle (threshold state)membrane voltage, V (mV)-40-50-60-70membrane voltage, V (mV)-60-70stable node (rest state)saddle-nodebifurcation-100 -50 0 50 100injected dc-current I4.51-10 -5 0 5 10injected dc-current IFigure 4.32: Saddle-node bifurcation diagram of the I Na,p +I K -model.given by the equation (4.13).The curve ismembrane voltage, V (mV)injected current, I0-20-40-60-80302010resttransition(bifurcation)I=12spiking00 10 20 30 40 50 60 70 80 90 100time (ms)Figure 4.33: Transition from rest state to repetitive spiking in the I Na,p +I K -modelwith ramp injected current I; see also Fig. 4.34 (small-amplitude noise is added tothe model to mask the slow passage effect). Notice that the frequency of spiking isrelatively constant for a wide range of injected current.