Energy localization and transport in two-dimensional electrical lattices

Abstract

Intrinsic localized modes (ILMs) have been generated and characterized in two-dimensional nonlinear electrical lattices which were driven by a spatially-uniform voltage signal. These ILMs were found to be either stationary or mobile, depending on the details of the lattice unit-cell, as had already been reported in one-dimensional lattices; however, the mo- tion of these ILMs is qualitatively di erent in that it lacks a consistent direction. Furthermore, the hop- ping speed seems to be somewhat reduced in two di- mensions due to an enhanced Peierls-Nabarro (PN)- barrier. We investigate both square and honeycomb lattices composed of 6 x 6 elements. These direct ob- servations were further supported by numerical simu- lations based on realistic models of circuit components. The numerical study moreover allowed for an analysis of ILM dynamics and pattern formation for larger lat- tice sizes.