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, GermanyValentín FlunkertInstitut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, GermanyStephen W. TeitsworthDepartment of Physics, Duke University, PO Box 90305, Durham, NC 27708-0305, USA
2016en
ABI
Abstract
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.
Citations and references
Cited by 20 references