Dynamical Systems in Neuroscience:

138 Conductance-Based Models1I=01I=0K + activation, n0.80.60.40 15n-nullclineK + activation, n0.80.60.4n-nullcline0 15V-nullclineV-nullcline0.20.200-60 -20 0 20membrane voltage, V-60 20membrane voltage, V1I=101I=40K + activation, n0.80.60.40 15n-nullclineK + activation, n0.80.60.4n-nullcline0 15V-nullclineV-nullcline0.20.200-60 -20 0 20membrane voltage, Va-60 -20 0 20membrane voltage, VbFigure 5.4: Possible forms of nullclines in the I Na,p +I K -model. Parameters as in theprevious chapter (see caption to Fig. 4.1).rather unexpected mechanisms for voltage oscillations. Nevertheless, it is educationalto consider all 6 models to see how the theory of dynamical systems works whereintuition and common sense fail.5.1.2 I Na,p +I K -modelOne of the most fundamental models in computational neuroscience is the I Na,p +I K -model consisting of a fast Na + current and a relatively slower K + current:I Na,pleak I LIC ˙V{ }} { { }} { { }} K{= I − g L (V −E L ) − g Na m(V − E Na ) − g K n(V − E K ) ,ṁ = (m ∞ (V ) − m)/τ m (V ) ,ṅ = (n ∞ (V ) − n)/τ n (V ) .