Almost Complete and Equable Heteroclinic Networks

• Tipo: Artigo em Revista Científica Internacional
• Data: 2020

Autores

Ashwin, P (Autor) Outra; Castro, SBSD (Autor) FEP; Lohse, A (Autor) Outra

Revista

Título: Journal of Nonlinear Science

Vol. 30

Páginas: 1-22

ISSN: 0938-8974

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 13 Citações

Scopus - 14 Citações

Outras Informações

ID Authenticus: P-00Q-WVJ

DOI: 10.1007/s00332-019-09566-z

Abstract (EN): Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces. In this paper, we examine the relation between the heteroclinic network as a flow-invariant set and directed graphs of possible connections between nodes. We consider realizations of a large class of transitive digraphs as robust heteroclinic networks and show that although robust realizations are typically not complete (i.e. not all unstable manifolds of nodes are part of the network), they can be almost complete (i.e. complete up to a set of zero measure within the unstable manifold) and equable (i.e. all sets of connections from a node have the same dimension). We show there are almost complete and equable realizations that can be closed by adding a number of extra nodes and connections. We discuss some examples and describe a sense in which an equable almost complete network embedding is an optimal description of stochastically perturbed motion on the network.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 22