Nonlinear localized modes in two-dimensional electrical lattices

TL;DR

This paper demonstrates the experimental and theoretical observation of localized energy modes in two-dimensional nonlinear electrical lattices, revealing stable stationary and traveling discrete breathers influenced by nonlinearity, damping, and driving.

Contribution

It introduces the first experimental realization of stationary and traveling discrete breathers in 2D electrical lattices, with controllable induction and complex interactions.

Findings

Stable stationary discrete breathers exist in specific voltage and frequency regions.

Traveling breathers can be induced by adding capacitors to the lattice.

Numerical simulations agree with experimental observations and scale to larger lattices.

Abstract

We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and traveling self-localized modes were generated experimentally and theoretically in a family of two-dimensional square, as well as hon- eycomb lattices composed of 6x6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILM), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introduc- ing additional capacitors into the unit cell, these lattices can controllably induce traveling discrete breathers. When more than one such ILMs are experimentally generated in the lattice, the interplay of nonlinearity, discreteness and wave interactions generate a complex dynamics wherein the ILMs attempt to maintain a minimum distance between one another. Numerical simulations show good agreement with experimental results, and confirm that these phenomena qualitatively carry over to larger lattice sizes.