Fast–Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes

The Journal of Mathematical Neuroscience

Table 1 Abbreviations

Name	Alternative names	Abbreviation
Codim-1 Bifurcations
Saddle-Node	Fold, tangential, limit point	SN
Saddle-Node on Invariant Circle	Saddle-node-loop of codim-1	SNIC
Hopf	Poincaré–Andronov–Hopf	H
Saddle Homoclinic	Saddle loop, homoclinic connection	SH
Fold Limit Cycle	Double cycle, fold of cycles, saddle-node of limit cycles, saddle node of periodic orbits	FLC
subcritical/supercritical		sub/sup
Codim-2 Bifurcations
Cusp		C
Bautin	Degenerate Hopf–Takens, generalized Hopf	B
Takens–Bogdanov		TB
Degenerate Loop	Neutral-saddle-homoclinic loop	DL
Saddle-Node-Loop		SNL
Codim-3 Bifurcations
degenerate Takens–Bogdanov		deg. TB
Regions in the bifurcation diagram
Limit Cycle small—silent state outside the stable limit cycle		LCs
Limit Cycle big—stable limit cycle surrounds the silent state		LCb
Other relevant points in the bifurcation diagram (not bifurcation points)
H and SN occur on two different fixed points		P_1,2
FLC and SN occur for the same parameters’ values		P₃

We report the abbreviations used in this manuscript for bifurcations and regions in the bifurcation diagram. For the bifurcations we report alternative names available in the literature.