Symmetry-breaking transitions in networks of nonlinear circuit elements

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.

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

References in corpus (9)

• Semiconductor Superlattices: A model system for nonlinear transport
• Delayed feedback as a means of control of noise-induced motion
• Time-delayed feedback in neurosystems
• Dynamics of delay-coupled excitable neural systems
• Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback
• Self-organized stable pacemakers near the onset of birhythmicity
• Resonant control of stochastic spatio-temporal dynamics in a tunnel diode by multiple time delayed feedback
• Lateral current density fronts in asymmetric double-barrier resonant-tunneling structures
• Emergence of current branches in a series array of negative differential resistance circuit elements

Cited by in corpus (21)

• When Nonlocal Coupling Between Oscillators Becomes Stronger: Patched Synchrony or Multi-Chimera States
• Chimera Death: Symmetry Breaking in Dynamical Networks
• Coherence-resonance chimeras in a network of excitable elements
• Asymmetric balance in symmetry breaking
• Experimental observation of a transition from amplitude to oscillation death in coupled oscillators
• Amplitude death in oscillator networks with variable-delay coupling
• Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines
• Stable and transient multi-cluster oscillation death in nonlocally coupled networks
• Distinct collective states due to the trade-off between attractive and repulsive couplings
• Partial Synchronization and Partial Amplitude Death in Mesoscale Network Motifs
• Delay-induced chimeras in neural networks with fractal topology
• Heterogeneous Delays in Neural Networks
• Unbalanced clustering and solitary states in coupled excitable systems
• Synchronization in heterogeneous FitzHugh-Nagumo networks with hierarchical architecture
• Adaptive control of synchronization in delay-coupled heterogeneous networks of FitzHugh-Nagumo nodes
• Bistability in Two Simple Symmetrically Coupled Oscillators with Symmetry-broken Amplitude- and Phase-Locking
• Dynamical order, disorder and propagating defects in homogeneous system of relaxation oscillators
• Saddle-node bifurcations for concave in measure and d-concave in measure skewproduct flows with applications to population dynamics and circuits
• Oscillation quenching in third order Phase Locked Loop coupled by mean field diffusive coupling
• A Simple Electronic Circuit Demonstrating Hopf Bifurcation for an Advanced Undergraduate Laboratory
• Bifurcations of Clusters and Collective Oscillations in Networks of Bistable Units