7,832 research outputs found
Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling
Small lattices of nearest neighbor coupled excitable FitzHugh-Nagumo
systems, with time-delayed coupling are studied, and compared with systems of
FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of
equilibria in N=2 case are studied analytically, and it is then numerically
confirmed that the same bifurcations are relevant for the dynamics in the case
. Bifurcations found include inverse and direct Hopf and fold limit cycle
bifurcations. Typical dynamics for different small time-lags and coupling
intensities could be excitable with a single globally stable equilibrium,
asymptotic oscillatory with symmetric limit cycle, bi-stable with stable
equilibrium and a symmetric limit cycle, and again coherent oscillatory but
non-symmetric and phase-shifted. For an intermediate range of time-lags inverse
sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of
oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo
oscillators with the same type of coupling.Comment: accepted by Phys.Rev.
Optimizing periodicity and polymodality in noise-induced genetic oscillators
Many cellular functions are based on the rhythmic organization of biological
processes into self-repeating cascades of events. Some of these periodic
processes, such as the cell cycles of several species, exhibit conspicuous
irregularities in the form of period skippings, which lead to polymodal
distributions of cycle lengths. A recently proposed mechanism that accounts for
this quantized behavior is the stabilization of a Hopf-unstable state by
molecular noise. Here we investigate the effect of varying noise in a model
system, namely an excitable activator-repressor genetic circuit, that displays
this noise-induced stabilization effect. Our results show that an optimal noise
level enhances the regularity (coherence) of the cycles, in a form of coherence
resonance. Similar noise levels also optimize the multimodal nature of the
cycle lengths. Together, these results illustrate how molecular noise within a
minimal gene regulatory motif confers robust generation of polymodal patterns
of periodicity.Comment: 9 pages, 6 figure
Dynamical effects induced by long range activation in a nonequilibrium reaction-diffusion system
We both show experimentally and numerically that the time scales separation
introduced by long range activation can induce oscillations and excitability in
nonequilibrium reaction-diffusion systems that would otherwise only exhibit
bistability. Namely, we show that the Chlorite-Tetrathionate reaction, where
autocatalytic species diffuses faster than the substrates, the spatial
bistability domain in the nonequilibrium phase diagram is extended with
oscillatory and excitability domains. A simple model and a more realistic model
qualitatively account for the observed behavior. The latter model provides
quantitative agreement with the experiments.Comment: 19 pages + 9 figure
A comparison of methods to determine neuronal phase-response curves
The phase-response curve (PRC) is an important tool to determine the
excitability type of single neurons which reveals consequences for their
synchronizing properties. We review five methods to compute the PRC from both
model data and experimental data and compare the numerically obtained results
from each method. The main difference between the methods lies in the
reliability which is influenced by the fluctuations in the spiking data and the
number of spikes available for analysis. We discuss the significance of our
results and provide guidelines to choose the best method based on the available
data.Comment: PDFLatex, 16 pages, 7 figures
Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?
We present a bifurcation analysis of a normal form for travelling waves in
one-dimensional excitable media. The normal form which has been recently
proposed on phenomenological grounds is given in form of a differential delay
equation. The normal form exhibits a symmetry preserving Hopf bifurcation which
may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry
breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf
bifurcation for the propagation of a single pulse in a ring by means of a
center manifold reduction, and for a wave train by means of a multiscale
analysis leading to a real Ginzburg-Landau equation as the corresponding
amplitude equation. Both, the center manifold reduction and the multiscale
analysis show that the Hopf bifurcation is always subcritical independent of
the parameters. This may have links to cardiac alternans which have so far been
believed to be stable oscillations emanating from a supercritical bifurcation.
We discuss the implications for cardiac alternans and revisit the instability
in some excitable media where the oscillations had been believed to be stable.
In particular, we show that our condition for the onset of the Hopf bifurcation
coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao
Chaotic Observer-based Synchronization Under Information Constraints
Limit possibilities of observer-based synchronization systems under
information constraints (limited information capacity of the coupling channel)
are evaluated. We give theoretical analysis for multi-dimensional
drive-response systems represented in the Lurie form (linear part plus
nonlinearity depending only on measurable outputs). It is shown that the upper
bound of the limit synchronization error (LSE) is proportional to the upper
bound of the transmission error. As a consequence, the upper and lower bounds
of LSE are proportional to the maximum rate of the coupling signal and
inversely proportional to the information transmission rate (channel capacity).
Optimality of the binary coding for coders with one-step memory is established.
The results are applied to synchronization of two chaotic Chua systems coupled
via a channel with limited capacity.Comment: 7 pages, 6 figures, 27 reference
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