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Table 4 Bursting classes far from the deg. TB singularity, focus case

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

Class

Label

Bifurcations sequence

Point A

Point B

LCs region

SN/FLC

c4s

SN l , FLC B , SN r ; SN l , FLC B , subH, SN r

SN l [TB l , C s ]

SN r [P3, SNLs r ]

supH/FLC

c12s

SN l , FLC B , subH, supH, SN r

SN l [TB l , C s ]

SN r [C s , P3]

subH/SH

c14s

SH l , subH, FLC B , SN r

SH l

SN r [C s , P3]

subH/supH

c15s

SN l , supH, subH, FLC B , SN r

SN l [TB l , C s ]

SN r [C s , P3]

SNIC/FLC

c8b

H, SNIC l , FLC B , SN r , FLC B , SH l , SNIC, FLC B ; SN r , SH l , SNIC, FLC B

H [TB l , P2]

FLC B [P3, B2]

SN/SNIC

c1b

SN r , SH l , SNIC, SN r , SH l , H, SN r , FLC, SH l , SNIC, SN r , SH l , H

SN r [C s , P3]

H [TB l , P2]

SNIC/SNIC

c5b

SN r , SH l , SNIC, SNIC, H, SN r , FLC, SH l , SNIC, SNIC, H

SN r [C s , P3]

H [TB l , P2]

SNIC/SH

c6b

SN r , SH l , SH l , SN r , SNIC, H

SN r [C s , P3]

H [TB l , P2]

subH/SNIC

c13b

SN r , SH l , SNIC, H, SN r , FLC, SH l , SNIC, H,

SN r [C s , P3]

H [P2, B2]

  1. For each of the new classes found in the LCs region when increasing R we state the requirements in terms of sequence of bifurcations the system has to go through and location of initial and final points of the path. When more than one sequence is possible, they are all reported, but we did not verify that all the sequences could be obtained with paths as those described in the text for a given class.