358 research outputs found
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
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