Bifurcations of а separatrix loop of a sewn saddle-node in a generic two-parameter family of piecewise smooth vector fields
DOI:
https://doi.org/10.52575/2687-0959-2025-57-3-186-192Keywords:
Piecewise Smooth Vector Field, Saddle-Node, Separatrix Loop, Bifurcation, Stable Periodic TrajectoryAbstract
We consider a dynamical system on the plane defined by a piecewise smooth vector field. Let this vector field have a singular point S on the switching line such that in the neighborhood of S, on the one side of L, the field coincides with a smooth vector field for which S is a saddle-node with a stable parabolic sector and a central manifold transversal to L, and on the other side, it coincides with a smooth vector field transversal to L. It is also assumed that from the point S go a positive semitrajectory Γ, which does not contain singular points different from S and is limiting to S. We consider a generic two-parameter family of piecewise smooth vector fields, a deformation of the vector field under consideration. We describe a set of parameters for which a vector field from this family has a stable periodic trajectory born from a loop Γ.
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