Phase portrait Fitzugh-Nagumo model Gerstner & Kistler, Figure 3.2 Vertical Horizontal

Phase portraits new fixed points Khalil, Nonlinear Systems, Figures Real eigenvalues and eigenvectors Stable f.p. Unstable f.p. Complex eigenvalues and eigenvectors Saddle Real eigenvalues and eigenvectors

Linearization around a fixed point Gerstner & Kistler, Figure 3.3 Different system

Classification of fixed points Izhikevich, Figures 4.15 T

Limit cycle in FN model Gerstner & Kistler, Figure 3.4 Unstable fixed point

Stable fixed point and oscillation in the FN model Gerstner & Kistler, Figure 3.5 Stable fixed point – Zero input Limit cycle – Nonzero input (I=2) Upward shift of v-nullcline Single f.p. 3 f.p. Unstable fixed point

Nullclines of type I model Gerstner & Kistler, Figure 3.6 Zero input – 3 fixed points Nonzero input – 1 unstable fixed points Morris-Lecar model Stable Saddle Unstable

Gain functions for models of type I and II Gerstner & Kistler, Figure 3.7 Type I – continuous transition to oscillation Type II – discontinuous transition to oscillation

Threshold in type I model Gerstner & Kistler, Figure 3.9 Stable manifold of saddle-point No spike – below threshold Spike generated – above threshold Stable Saddle Unstable Morris-Lecar model

Threshold-like effect in FN Model (Type II) Gerstner & Kistler, Figure 3.7 For v 0 < trajectory returns rapidly to rest For v 0 > -0.1 a voltage pulse develops Amplitude of v(t) varies smoothly (was stereotyped for type I) Continuously varying behavior

FN model with separated time scales Vertical arrows: length O(ε) Plays the role of stable manifold (separating) Gerstner & Kistler, Figure 3.11

Separated time scales Gerstner & Kistler, Figure 3.12 Stereotyped action potential