Intrinsic Localized Modes in a Nonlinear Electrical Lattice with Saturable Nonlinearity

TL;DR

This experimental study investigates how saturable nonlinearity affects the behavior of intrinsic localized modes in an electronic lattice, revealing step-wise changes and hysteresis that influence ILM mobility.

Contribution

The paper provides experimental validation of theoretical predictions on ILMs in saturable nonlinear lattices, highlighting hysteresis effects on ILM dynamics.

Findings

ILMs are observed below the linear band due to soft nonlinearity.

Step-wise changes in ILM width and barrier softening are detected.

Hysteresis inhibits free ILM motion, contrary to some theoretical expectations.

Abstract

This experimental study of driven intrinsic localized modes (ILMs) in an electronic circuit lattice with saturable nonlinearity follows the theoretical work of Hadzievski and coworkers. They proposed that a saturable nonlinearity could introduce transition points where localized excitations in nonintegrable lattices would move freely. In our experiments MOS capacitors provide the saturable nonlinearity in an electric lattice. Because of the soft nonlinearity driver locked, auto-resonance stationary ILMs are observed below the bottom of a linear frequency band of the lattice. With decreasing driver frequency the width of the ILM changes in a step-wise manner as does the softening of the barrier between site-centered and bond-centered ILM locations in agreement with theoretical expectations. However, the steps show hysteresis between up and down frequency scans and such hysteresis inhibits the free motion of ILMs.