Dynamical Systems in Neuroscience:

262 ExcitabilityBogdanov-Takens bifurcationK + activation gate, n K + activation gate, n K + activation gate, n0.50.40.30.20.100.50.40.30.20.100.60.50.40.30.20.1n-nullclineV-nullcline-60 -40 -20 0V-nullcline-60 -40 -20 0n-nullclinen-nullclineK + activation gate, n K + activation gate, n K + activation gate, nintegrator (near saddle-node bifurcation)resonator (near Andronov-Hopf bifurcation)V-nullcline0.050.040.030.020.010-65 -60 -55 -500.050.040.030.020.01threshold0-65 -60 -55 -500.050.040.030.020.010-60 -40 -20 0membrane potential, V (mV)0-65 -60 -55 -50membrane potential, V (mV)Figure 7.39: Bogdanov-Takens bifurcation in the I Na +I K -model (4.1, 4.2). Parametersas in Fig. 4.1a, except n ∞ (V ) has k = 7 mV and V 1/2 = −31.64 mV, E leak = −79.42and I = 5. Integrator: V 1/2 = −31 mV and I = 4.3. Resonator: V 1/2 = −34 mV andI = 7.