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.