Switching in Heteroclinic Networks

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

Authors

Castro, SBSD (Author) FEP; Lohse, A (Author) Other

Journal

Title: SIAM Journal on Applied Dynamical Systems

Vol. 15 No. 2

Pages: 1085-1103

ISSN: 1536-0040

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 12 Citations

Scopus - 11 Citations

Other information

Authenticus ID: P-00K-M2G

DOI: 10.1137/15m1042176

Abstract (EN): We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the weakest forms of switching (i.e., along this connection). The form of the global transition maps, and thus the type of the heteroclinic cycle, plays a crucial role in this. We look at two examples in R-5, the House and Bowtie networks, to illustrate complex dynamics that may occur when either of these conditions is broken. For the House network, there is switching along the common connection, while for the Bowtie network we find switching along a cycle.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19