Nonlinear normal modes in a network with cubic couplings

We consider a network with cubic couplings. This is related to the well known Fermi-Pasta-Ulam-Tsingou model. We show that nonlinear periodic orbits extend from particular eigenvectors of the graph Laplacian, these are termed nonlinear normal modes . We present large classes of graphs where this occ...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 12; pp. 20565 - 20578
Main Authors Caputo, Jean-Guy, Khames, Imene, Knippel, Arnaud
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
fermi-pasta-ulam-tsingou (fput) model
graph laplacian
graph spectra and applications
networks
nonlinear normal mode (nnm)
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Summary:We consider a network with cubic couplings. This is related to the well known Fermi-Pasta-Ulam-Tsingou model. We show that nonlinear periodic orbits extend from particular eigenvectors of the graph Laplacian, these are termed nonlinear normal modes . We present large classes of graphs where this occurs. These are the graphs whose Laplacian eigenvectors have components in $ \{1, -1\} $ (bivalent), and $ \{1, -1, 0\} $ with a condition (soft-regular trivalent), the bipartite complete graphs and their extensions obtained by adding an edge between vertices having the same component. Finally, we study the stability of these solutions for chains and cycles.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20221127