Switching near a network of rotating nodes

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

Authors

Manuela A D Aguiar (Author) FEP; Isabel S Labouriau (Author) FCUP; Alexandre A P Rodrigues (Author) Other

Journal

Title: Dynamical Systems

Vol. 25 No. 1

Pages: 75-95

ISSN: 1468-9367

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 26 Citations

ISI Web of Science

Scopus - 25 Citations

Scientific classification

FOS: Engineering and technology > Mechanical engineering

Other information

Authenticus ID: P-003-AKT

DOI: 10.1080/14689360903252119

Abstract (EN): We study the dynamics of a Z(2) circle plus Z(2)-equivariant vector field in the neighbourhood of a heteroclinic network with a periodic trajectory and symmetric equilibria. We assume that around each equilibrium the linearization of the vector field has non-real eigenvalues. Trajectories starting near each node of the network turn around in space either following the periodic trajectory or due to the complex eigenvalues near the equilibria. Thus, in a network with rotating nodes, the rotations combine with transverse intersections of two-dimensional invariant manifolds to create switching near the network; close to the network, there are trajectories that visit neighbourhoods of the saddles following all the heteroclinic connections of the network in any given order. Our results are motivated by an example where switching was observed numerically by forced symmetry breaking of an asymptotically stable network with O(2) symmetry.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21