Symmetry-breaking transitions in networks of nonlinear circuit elements
Martin HeinrichDepartment of Physics, Duke University, PO Box 90305, Durham, NC 27708-0305, USAThomas DahmsInstitut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, GermanyValentin FlunkertInstitut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, GermanyStephen W TeitsworthDepartment of Physics, Duke University, PO Box 90305, Durham, NC 27708-0305, USAEckehard SchöllInstitut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
2010en
ABI
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.
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Cited by 20 references