Year: 2025
Type: article
Abstract: We consider generic families X θ of smooth dynamical systems depending on parameters θ ∈ P where P is a 2-dimensional simply connected domain and assume that each X θ only has a finite number of restpoints and periodic orbits. We prove that if over the boundary of P there is a S or Z shaped bifurcation graph containing two opposing fold bifurcation points while over the rest of the boundary there are no other bifurcation points, then, if there is no fold–Hopf bifurcation in P, there is a set of bifurcation curves in P that contain an odd number of cusps. In particular, there is at least one codimension 2 bifurcation point in the interior of P.
Source: Nonlinearity
Authors: D A Rand, M Sáez
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4408457693