Phonon Network Topology in Spatially Modulated Nonlinear Lattices

Even in the simplest structures, the presence of nonlinear phonon-phonon scattering can produce phonon dynamics of surprising complexity. The nonlinear resonances can be understood as forming an anharmonic network of coupled phonon modes. We examine the topology of these networks for a broad class of nonlinear lattices and show how the inclusion of a spatially modulated anharmonicity can produce large changes in this underlying topology. We further show how this graph topology impacts the dynamics of the coupled phonons.