WIAS Preprint No. 3133, (2024)

Reversible saddle-node separatrix-loop bifurcation


Authors

  • Burylko, Oleksandr
  • Wolfrum, Matthias
    ORCID: 0000-0002-4278-2675
  • Yanchuk, Serhiy

2020 Mathematics Subject Classification

  • 34C14 34C23 34C37

Keywords

  • Homoclinic bifurcations, time-reversibility

DOI

10.20347/WIAS.PREPRINT.3133

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.

Appeared in

  • Analytical and Approximate Methods for Complex Dynamical Systems, A. Timokha, ed., Understanding Complex Systems (UCS), Springer Nature Link, 2025, DOI 10.1007/978-3-031-77378-5_7 .

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