Networks of planar Hamiltonian systems

Tourigny, David S.

doi:10.1016/j.cnsns.2017.05.008

Cited by 2 publications

(1 citation statement)

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“…In Section 3, these results are applied to gradient and Hamiltonian coupled cell systems, in the context of the formalism of Golubitsky, Stewart and co-workers [15,11,10], where coupled cell systems are dynamical systems associated with graphs (coupled cell networks). Networks of gradient and Hamiltonian coupled systems have received some attention lately, see for example [5] and [13] for gradient networks and [6] and [16] for Hamiltonian networks, as well as references therein.…”

Section: Introductionmentioning

confidence: 99%

Quotients and lifts of symmetric directed graphs

Aguiar¹,

Dias²,

Manoel³

2018

Preprint

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Given a directed graph, an equivalence relation on the graph vertex set is said to be balanced if, for every two vertices in the same equivalence class, the number of directed edges from vertices of each equivalence class directed to each of the two vertices is the same. In this paper we describe the quotient and lift graphs of symmetric directed graphs associated with balanced equivalence relations on the associated vertex sets. In particular, we characterize the quotients and lifts which are also symmetric. We end with an application of these results to gradient and Hamiltonian coupled cell systems, in the context of the coupled cell network formalism of Golubitsky, Stewart and Török (Patterns of synchrony in coupled cell networks with multiple arrows. SIAM Journal of Applied Dynamical Systems 4 (1) (2005) 78-100).

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