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

2. Phase portraits new fixed points Khalil, Nonlinear Systems, Figures 2.3-2.7 Real eigenvalues and eigenvectors Stable f.p. Unstable f.p. Complex eigenvalues and eigenvectors Saddle Real eigenvalues and eigenvectors

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

4. Classification of fixed points Izhikevich, Figures 4.15 T

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

6. 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

7. 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

8. 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

9. 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

10. Threshold-like effect in FN Model (Type II) Gerstner & Kistler, Figure 3.7 For v 0 < -0.25 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

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

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