Stability of quasi-simple heteroclinic cycles

• Tipo: Artigo em Revista Científica Internacional
• Data: 2019

Autores

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

Revista

Título: Dynamical Systems

Vol. 34

Páginas: 14-39

ISSN: 1468-9367

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 13 Citações

Scopus - 14 Citações

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 26