Stability of quasi-simple heteroclinic cycles

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Garrido da Silva, L (Author) FEP; Castro, SBSD (Author) FEP

Journal

Title: Dynamical Systems

Vol. 34

Pages: 14-39

ISSN: 1468-9367

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 13 Citations

Scopus - 14 Citations

Other information

Authenticus ID: P-00P-Q49

DOI: 10.1080/14689367.2018.1445701

Abstract (EN): The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose connections are one-dimensional and contained in flow-invariant spaces of equal dimension. These heteroclinic cycles exist both in symmetric and non-symmetric contexts. We make one assumption on the dynamics along the connections to ensure that the transition matrices have a convenient form. Our method applies to all simple heteroclinic cycles of type Z and to various heteroclinic cycles arising in population dynamics, namely non-simple heteroclinic cycles, as well as to cycles that are part of a heteroclinic network. We illustrate our results with a non-simple cycle present in a heteroclinic network of the Rock-Scissors-Paper game.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 26