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Fig. 4 | The Journal of Mathematical Neuroscience (JMN)

Fig. 4

From: Neural Excitability and Singular Bifurcations

Fig. 4

Singular limit bifurcations at the lower fold \(F^{-}\) and their singular limit orbits in system (1) (\(v_{\mathrm {th}}>0\), \(I=I_{\mathrm{bif}}=0\)). (a) (Type I) singular saddle-node homoclinic (SNIC) (\(c=0\)) together with a singular Bogdanov–Takens bifurcation (= singular BT/SNIC); (b) singular Andronov–Hopf bifurcation with incomplete family of canard cycles (\(0< c< c_{\mathrm {sn}}\)); (c) family of (incomplete) canard cycles and family of singular saddle-node homoclinics of canard type (\(c=c_{\mathrm{sn}}\)); (d) (Type II) singular Andronov–Hopf bifurcation and (complete) family of canard cycles (\(c>c_{\mathrm{sn}}\))

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