@inbook{3c0b041f88b749c6831ab84af0f97212,
title = "Reversible Saddle-Node Separatrix-Loop Bifurcation",
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.",
keywords = "Bifurcation, Codimension-two, Coupled rotators, R-SNSL, SNIC, Time-reversibility",
author = "Oleksandr Burylko and Matthias Wolfrum and Serhiy Yanchuk",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.",
year = "2025",
doi = "10.1007/978-3-031-77378-5\_7",
language = "English",
series = "Understanding Complex Systems",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "101--119",
booktitle = "Understanding Complex Systems",
address = "Germany",
}