Symmetry-breaking transitions in networks of nonlinear circuit elements

TL;DR

This paper explores complex symmetry-breaking bifurcations in a nonlinear circuit of tunnel diodes modeled by FitzHugh-Nagumo systems, revealing multistability and degenerate bifurcations both theoretically and experimentally.

Contribution

It introduces a detailed analysis of symmetry-breaking bifurcations in a network of nonlinear circuit elements, combining theoretical bifurcation analysis with experimental validation.

Findings

Identification of symmetry-breaking bifurcations leading to multiple fixed points

Discovery of degenerate zero-eigenvalue bifurcations causing multistability

Experimental confirmation of bifurcation scenarios predicted theoretically

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.