Reversible Saddle-Node Separatrix-Loop Bifurcation

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Abstract

We describe the unfolding of a special variant of the codimension-two Saddle-Node Separatrix-Loop (SNSL) bifurcation that occurs in systems with time-reversibility. While the classical SNSL bifurcation can be characterized as the collision of a saddle-node equilibrium with a limit cycle, the reversible variant (R-SNSL) is characterised by as the collision of a saddle-node equilibrium with a boundary separating a dissipative and a conservative region in phase space. Moreover, we present several reversible versions of the SNIC (Saddle-Node on Invariant Circle) bifurcation and discuss the role of an additional reversible saddle equilibrium in all these scenarios. As an example, we provide a detailed bifurcation scenario for a reversible system of two coupled phase rotators (a system on a 2D torus) involving a R-SNSL bifurcation.

Original languageEnglish
Title of host publicationUnderstanding Complex Systems
PublisherSpringer Science and Business Media Deutschland GmbH
Pages101-119
Number of pages19
DOIs
Publication statusPublished - 2025

Publication series

NameUnderstanding Complex Systems
VolumePart F192
ISSN (Print)1860-0832
ISSN (Electronic)1860-0840

Keywords

  • Bifurcation
  • Codimension-two
  • Coupled rotators
  • R-SNSL
  • SNIC
  • Time-reversibility

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