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

Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.Comment: 18 pages, 14 figure

Excitation of solitons in hexagonal lattices and ways of controlling electron transport

This is a post-peer-review, pre-copyedit version of an article published in Philosophical Transactions A: Mathematical, Physical and Engineering Sciences. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40435-017-0383-x.We construct metastable long-living hexagonal lattices with appropriately modified Morse interactions and show that highly-energetic solitons may be excited moving along crystallographic axes. Studying the propagation, their dynamic changes and the relaxation processes it appears that lump solitons create in the lattice running local compressions. Based on the tight-binding model we investigate the possibility that electrons are trapped and guided by the electric polarization field of the compression field of one soliton or two solitons with crossing pathways. We show that electrons may jump from a bound state with the first soliton to a bound state with a second soliton and changing accordingly the direction of their path. We discuss the possibility to control by this method the path of an excess electron from a source at a boundary to a selected drain at another chosen boundary by following straight pathways on crystallographic axes.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Coherence resonance in a network of FitzHugh-Nagumo systems: interplay of noise, time-delay and topology

We systematically investigate the phenomena of coherence resonance in time-delay coupled networks of FitzHugh-Nagumo elements in the excitable regime. Using numerical simulations, we examine the interplay of noise, time-delayed coupling and network topology in the generation of coherence resonance. In the deterministic case, we show that the delay-induced dynamics is independent of the number of nearest neighbors and the system size. In the presence of noise, we demonstrate the possibility of controlling coherence resonance by varying the time-delay and the number of nearest neighbors. For a locally coupled ring, we show that the time-delay weakens coherence resonance. For nonlocal coupling with appropriate time-delays, both enhancement and weakening of coherence resonance are possible

Effects of external global noise on the catalytic CO oxidation on Pt(110)

Oxidation reaction of CO on a single platinum crystal is a reaction-diffusion system that may exhibit bistable, excitable, and oscillatory behavior. We studied the effect of a stochastic signal artificially introduced into the system through the partial pressure of CO. First, the external signal is employed as a turbulence suppression tool, and second, it modifies the boundaries in the bistable transition between the CO and oxygen covered phases. Experiments using photoemission electron microscopy (PEEM) together with numerical simulations performed with the Krischer-Eiswirth-Ertl (KEE) model are presented.Comment: 15 pages, 7 figures, accepted in J. Chem. Phy

Delayed feedback control of self-mobile cavity solitons in a wide-aperture laser with a saturable absorber

We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed optical feedback. Using a combination of analytical, numerical and path continuation methods we analyze the bifurcation structure of stationary and moving cavity solitons and identify two different types of traveling localized solutions, corresponding to slow and fast motion. We show that the delay impacts both stationary and moving solutions either causing drifting and wiggling dynamics of initially stationary cavity solitons or leading to stabilization of intrinsically moving solutions. Finally, we demonstrate that the fast cavity solitons can be associated with a lateral mode-locking regime in a broad-area laser with a single longitudinal mode

Time--delay autosynchronization of the spatio-temporal dynamics in resonant tunneling diodes

The double barrier resonant tunneling diode exhibits complex spatio-temporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time--delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way. We compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom. The numerically obtained Floquet exponents are explained by analytical results from linear stability analysis.Comment: 10 pages, 16 figure

Synchronization of chaotic networks with time-delayed couplings: An analytic study

Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli maps, analytic results are derived for the stability of the chaotic synchronization manifold. For a single delay time, chaos synchronization is related to the spectral gap of the coupling matrix. For networks with multiple delay times, analytic results are obtained from the theory of polynomials. Finally, the analytic results are compared with networks of iterated tent maps and Lang-Kobayashi equations which imitate the behaviour of networks of semiconductor lasers