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The realisation of admissible graphs for coupled vector fields

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Autor(es):
Amorim, Tiago de Albuquerque ; Manoel, Miriam
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: Nonlinearity; v. 37, n. 1, p. 26-pg., 2024-12-14.
Resumo

In a coupled network cells can interact in several ways. There is a vast literature from the last 20 years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence relation on the set of vertices that enables a characterisation of the admissible vector fields that rules the network dynamics. The present work goes in the direction of answering an inverse problem: for n > 2 , any mapping on Rn can be realised as an admissible vector field for some graph with the number of vertices depending on (but not necessarily equal to) n. Given a mapping, we present a procedure to construct all non-equivalent admissible graphs, up to the appropriate equivalence relation. We also give an upper bound for the number of such graphs. As a consequence, invariant subspaces under the vector field can be investigated as the locus of synchrony states supported by an admissible graph, in the sense that a suitable graph can be chosen to realise couplings with more (or less) synchrony than another graph admissible to the same vector field. The approach provides in particular a systematic investigation of occurrence of chimera states in a network of van der Pol identical oscillators. (AU)

Processo FAPESP: 19/21181-0 - Novas fronteiras na Teoria de Singularidades
Beneficiário:Regilene Delazari dos Santos Oliveira
Modalidade de apoio: Auxílio à Pesquisa - Temático