Bistable boundary conditions implying codimension 2 bifurcations
Other authors
Publication date
2025-03-14ISSN
1361-6544
Abstract
We consider generic families Xθ of smooth dynamical systems depending on parameters θ ∈ P where P is a 2-dimensional simply connected domain and assume that each Xθ 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.
Document Type
Article
Document version
Published version
Language
English
Subject (CDU)
51 - Mathematics
Keywords
Dynamical systems
Bifurcations
Catastrophes
Cusp bifurcation
Bogdanov-Takens bifurcation
Dinàmica
Bifurcació, Teoria de la
Catàstrofes (Matemàtica)
Pages
p.14
Publisher
IOP Publishing i London Mathematical Society
Is part of
Nonlinearity 2025, 38
This item appears in the following Collection(s)
Rights
© L'autor/a
Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by/4.0/