Symmetry-breaking transitions in networks of nonlinear circuit elements
Abstract
We investigate a nonlinear circuit consisting of N tunnel diodes in series, which shows close similarities to a semiconductor superlattice or to a neural network. Each tunnel diode is modeled by a three-variable FitzHugh-Nagumo-like system. The tunnel diodes are coupled globally through a load resistor. We find complex bifurcation scenarios with symmetry-breaking transitions that generate multiple fixed points off the synchronization manifold. We show that multiply degenerate zero-eigenvalue bifurcations occur, which lead to multistable current branches, and that these bifurcations are also degenerate with a Hopf bifurcation. These predicted scenarios of multiple branches and degenerate bifurcations are also found experimentally.
Keywords
Cite
@article{arxiv.1006.5042,
title = {Symmetry-breaking transitions in networks of nonlinear circuit elements},
author = {Martin Heinrich and Thomas Dahms and Valentin Flunkert and Stephen W. Teitsworth and Eckehard Schöll},
journal= {arXiv preprint arXiv:1006.5042},
year = {2010}
}
Comments
32 pages, 11 figures, 7 movies available as ancillary files