A heteroclinic network in mode interaction with symmetry

• Type: Article in International Scientific Journal
• Date: 2010

Authors

Sofia B. S. D. Castro (Author) FEP; Labouriau, IS (Author) FCUP; Olga Podvigina (Author) Other

Journal

Title: Dynamical Systems

Vol. 25 No. 3

Pages: 359-396

ISSN: 1468-9367

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 11 Citations

ISI Web of Science

Scopus - 9 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-AKV

DOI: 10.1080/14689367.2010.506183

Abstract (EN): We study a robust heteroclinic network existing in generic mode interactions of symmetric dynamical systems. Each mode lies in C(3) and is equivariant under the action of D(6) x T(2) x Z(2). With this symmetry there are eight different types of non-trivial steady states. This work is motivated by Boussinesq convection on a plane layer with periodic boundary conditions on a hexagonal lattice. The mode interaction takes place in a centre eigenspace isomorphic to C(6) when the trivial steady state becomes unstable to two modes of the form of rolls with spatial periods in the 2 : root 3 ratio. Due to relations between the normal form coefficients, only four types of steady states can be involved in the network. We examine the normal form restricted to R(6), a flow-invariant subspace, then we describe the dynamics near the network and discuss subnetworks and switching near them.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 38