388 research outputs found
Robust chimera states in SQUID metamaterials with local interactions
We report on the emergence of robust multi-clustered chimera states in a
dissipative-driven system of symmetrically and locally coupled identical SQUID
oscillators. The "snake-like" resonance curve of the single SQUID
(Superconducting QUantum Interference Device) is the key to the formation of
the chimera states and is responsible for the extreme multistability exhibited
by the coupled system that leads to attractor crowding at the geometrical
resonance (inductive-capacitive) frequency. Until now, chimera states were
mostly believed to exist for nonlocal coupling. Our findings provide
theoretical evidence that nearest neighbor interactions are indeed capable of
supporting such states in a wide parameter range. SQUID metamaterials are the
subject of intense experimental investigations and we are highly confident that
the complex dynamics demonstrated in this manuscript can be confirmed in the
laboratory
Delay-induced multistability near a global bifurcation
We study the effect of a time-delayed feedback within a generic model for a
saddle-node bifurcation on a limit cycle. Without delay the only attractor
below this global bifurcation is a stable node. Delay renders the phase space
infinite-dimensional and creates multistability of periodic orbits and the
fixed point. Homoclinic bifurcations, period-doubling and saddle-node
bifurcations of limit cycles are found in accordance with Shilnikov's theorems.Comment: Int. J. Bif. Chaos (2007), in prin
The Effect of Intra- and Inter-ring Couplings in Leaky Integrate-and-Fire Multiplex Networks
We study the dynamics of identical Leaky Integrate-and-Fire (LIF) neurons on
a multiplex composed of two ring networks with symmetric nonlocal coupling
within each ring and one-to-one connections between rings. We investigate the
impact of different intra-ring coupling strengths in the two rings for
attractive and repulsive inter-ring coupling and show that they can lead to
subthreshold oscillations. The corresponding parameter spaces where this
phenomenon occurs are determined numerically. Moreover, we show that depending
on whether the couplings between the two rings are attractive or repulsive, the
interaction produces qualitatively different behavior in the synchronization
patterns and the mean frequency profiles.Comment: 12 pages; 6 figure
Chimeras in Leaky Integrate-and-Fire Neural Networks: Effects of Reflecting Connectivities
The effects of nonlocal and reflecting connectivity are investigated in
coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange
of electrical signals between neurons. Earlier investigations have demonstrated
that non-local and hierarchical network connectivity often induces complex
synchronization patterns and chimera states in systems of coupled oscillators.
In the LIF system we show that if the elements are non-locally linked with
positive diffusive coupling in a ring architecture the system splits into a
number of alternating domains. Half of these domains contain elements, whose
potential stays near the threshold, while they are interrupted by active
domains, where the elements perform regular LIF oscillations. The active
domains move around the ring with constant velocity, depending on the system
parameters. The idea of introducing reflecting non-local coupling in LIF
networks originates from signal exchange between neurons residing in the two
hemispheres in the brain. We show evidence that this connectivity induces novel
complex spatial and temporal structures: for relatively extensive ranges of
parameter values the system splits in two coexisting domains, one domain where
all elements stay near-threshold and one where incoherent states develop with
multileveled mean phase velocity distribution.Comment: 12 pages, 12 figure
Multi-channel pulse dynamics in a stabilized Ginzburg-Landau system
We study the stability and interactions of chirped solitary pulses in a
system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a
group-velocity mismatch between them, where each CGL equation is stabilized by
linearly coupling it to an additional linear dissipative equation. In the
context of nonlinear fiber optics, the model describes transmission and
collisions of pulses at different wavelengths in a dual-core fiber, in which
the active core is furnished with bandwidth-limited gain, while the other,
passive (lossy) one is necessary for stabilization of the solitary pulses.
Complete and incomplete collisions of pulses in two channels in the cases of
anomalous and normal dispersion in the active core are analyzed by means of
perturbation theory and direct numerical simulations. It is demonstrated that
the model may readily support fully stable pulses whose collisions are
quasi-elastic, provided that the group-velocity difference between the two
channels exceeds a critical value. In the case of quasi-elastic collisions, the
temporal shift of pulses, predicted by the analytical approach, is in
semi-quantitative agrement with direct numerical results in the case of
anomalous dispersion (in the opposite case, the perturbation theory does not
apply). We also consider a simultaneous collision between pulses in three
channels, concluding that this collision remains quasi-elastic, and the pulses
remain completely stable. Thus, the model may be a starting point for the
design of a stabilized wavelength-division-multiplexed (WDM) transmission
system.Comment: a text file in the revtex4 format, and 16 pdf files with figures.
Physical Review E, in pres
Metastable and chimera-like states in the C.elegans brain network
We model the neuronal activity of the C.elegans network by coupling Hindmarsh-Rose oscillators through the adjacency matrix obtained from its corresponding brain connectivity. By means of numerical simulations, we produce the parameter spaces for quantities related to synchronization, metastability and chimera-like dynamics, identifying, thus, interesting complex patterns of collective behaviour
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