Symmetry-breaking transitions in networks of nonlinear circuit elements

Journal Article

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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Full Text

Duke Authors

Cited Authors

  • Heinrich, M; Dahms, T; Flunkert, V; Teitsworth, SW; Schöll, E

Published Date

  • 2010

Published In

Volume / Issue

  • 12 /

International Standard Serial Number (ISSN)

  • 1367-2630

Digital Object Identifier (DOI)

  • 10.1088/1367-2630/12/11/113030