Symmetry-breaking transitions in networks of nonlinear circuit elements

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.Comment: 32 pages, 11 figures, 7 movies available as ancillary file

Chaos synchronization in networks of delay-coupled lasers: Role of the coupling phases

We derive rigorous conditions for the synchronization of all-optically coupled lasers. In particular, we elucidate the role of the optical coupling phases for synchronizability by systematically discussing all possible network motifs containing two lasers with delayed coupling and feedback. Hereby we explain previous experimental findings. Further, we study larger networks and elaborate optimal conditions for chaos synchronization. We show that the relative phases between lasers can be used to optimize the effective coupling matrix.Comment: 21 pages, 10 figure

Neural forecasting: Introduction and literature overview

Neural network based forecasting methods have become ubiquitous in large-scale industrial forecasting applications over the last years. As the prevalence of neural network based solutions among the best entries in the recent M4 competition shows, the recent popularity of neural forecasting methods is not limited to industry and has also reached academia. This article aims at providing an introduction and an overview of some of the advances that have permitted the resurgence of neural networks in machine learning. Building on these foundations, the article then gives an overview of the recent literature on neural networks for forecasting and applications.Comment: 66 pages, 5 figure