Nonlinear normal modes in a network with cubic couplings

• Published in: AIMS mathematics Vol. 7; no. 12; pp. 20565 - 20578
• Main Authors: Caputo, Jean-Guy, Khames, Imene, Knippel, Arnaud
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2022
• Subjects: fermi-pasta-ulam-tsingou (fput) model; graph laplacian; graph spectra and applications; networks; nonlinear normal mode (nnm)
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.20221127

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...