Arbitrarily large heteroclinic networks in fixed low-dimensional state space

• Type: Article in International Scientific Journal
• Date: 2023

Authors

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

Journal

Title: Chaos

Vol. 33

ISSN: 1054-1500

Publisher: American Institute of Physics

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00Z-13P

DOI: 10.1063/5.0156192

Abstract (EN): We consider heteroclinic networks between n & ISIN; N nodes where the only connections are those linking each node to its two subsequent neighboring ones. Using a construction method where all nodes are placed in a single one-dimensional space and the connections lie in coordinate planes, we show that it is possible to robustly realize these networks in R- 6 for any number of nodes n using a polynomial vector field. This bound on the space dimension (while the number of nodes in the network goes to 8) is a novel phenomenon and a step toward more efficient realization methods for given connection structures in terms of the required number of space dimensions. We briefly discuss some stability properties of the generated heteroclinic objects.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16