Hopf Bifurcation with Tetrahedral and Octahedral Symmetry

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Isabel S Labouriau (Author) FCUP; Murza, AC (Author) Other

Journal

Title: SIAM Journal on Applied Dynamical Systems

Vol. 15

Pages: 125-141

ISSN: 1536-0040

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00K-DG0

DOI: 10.1137/15m1009317

Abstract (EN): In the study of the periodic solutions of a G-equivariant dynamical system, the H mod K theorem gives all possible periodic solutions, based on group-theoretical aspects. By contrast, the equivariant Hopf theorem guarantees the existence of families of small-amplitude periodic solutions bifurcating from the origin for each C-axial subgroup of Gamma x S-1. In this article we compare the bifurcation of periodic solutions for generic differential equations equivariant under the full group of symmetries of the tetrahedron and the group of rotational symmetries of the cube. The two groups are the image of inequivalent representations of the symmetric group S-4. The possible spatial symmetries of bifurcating solutions are different, even though the two groups yield the same group of matrices Gamma x S-1. The same group of matrices occurs again as the extension Gamma x S-1 when G is the full group of symmetries of the cube. For these three groups, while characterizing the Hopf bifurcation, we identify which periodic solution types, whose existence is guaranteed by the H mod K theorem, are obtainable by Hopf bifurcation from the origin.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17