Symmetry-breaking transitions in networks of nonlinear circuit elements

Details Symmetry-breaking transitions in networks of nonlinear circuit elements Symmetry-breaking transitions in networks of nonlinear circuit elements

2010-06-24

arxiv.org/abs/1006.5042v4

New J. Phys. 12, 113030 (2010)

Nonlinear Sciences

Chaotic Dynamics

32 pages, 11 figures, 7 movies available as ancillary files

Scientific paper

10.1088/1367-2630/12/11/113030

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.

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