Reversible Saddle-Node Separatrix-Loop bifurcation

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Date
2025-03-17
Authors
Burylko, Oleksandr
Wolfrum, Matthias
Yanchuk, Serhiy
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Springer Nature
Published Version
10.1007/978-3-031-77378-5_7
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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.
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Keywords
Saddle-Node Separatrix-Loop , Bifurcation , Saddle-Node on Invariant Circle , Time-reversibility , Coupled rotators , R-SNSL , Codimension-two , SNIC
Citation
Burylko, O., Wolfrum, M. and Yanchuk, S. (2025) 'Reversible Saddle-Node Separatrix-Loop bifurcation', in Timokha, A. (ed) Analytical and Approximate Methods for Complex Dynamical Systems. Understanding Complex Systems. Springer, Cham. p. 101–119. https://doi.org/10.1007/978-3-031-77378-5_7
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https://hdl.handle.net/10468/17352
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© 2025, The Authors, under exclusive license to Springer Nature Switzerland AG. This version of the paper has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/978-3-031-77378-5_7