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Book Chapter

Reversible Saddle-Node Separatrix-Loop Bifurcation

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/persons/resource/oleksandr.burylko

Burylko,  Oleksandr
Potsdam Institute for Climate Impact Research;

Wolfrum,  Matthias
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/persons/resource/yanchuk

Yanchuk,  Serhiy       
Potsdam Institute for Climate Impact Research;

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Citation

Burylko, O., Wolfrum, M., Yanchuk, S. (2025): Reversible Saddle-Node Separatrix-Loop Bifurcation. - In: Timokha, A. (Ed.), Analytical and Approximate Methods for Complex Dynamical Systems, (Understanding Complex Systems), Cham : Springer, 101-119.
https://doi.org/10.1007/978-3-031-77378-5_7


Cite as: https://publications.pik-potsdam.de/pubman/item/item_33118
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.