Energy localization and transport in two-dimensional electrical lattices

Abstract

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 motion of these ILMs is qualitatively different in that it lacks a consistent direction. Furthermore, the hopping speed seems to be somewhat reduced in two dimensions due to an enhanced Peierls-Nabarro (PN)-barrier. We investigate both square and honeycomb lattices composed of 6 × 6 elements. These direct observations were further supported by numerical simulations based on realistic models of circuit components. The numerical study moreover allowed for an analysis of ILM dynamics and pattern formation for larger lattice sizes.