84 research outputs found
Collective dynamics of two-mode stochastic oscillators
We study a system of two-mode stochastic oscillators coupled through their
collective output. As a function of a relevant parameter four qualitatively
distinct regimes of collective behavior are observed. In an extended region of
the parameter space the periodicity of the collective output is enhanced by the
considered coupling. This system can be used as a new model to describe
synchronization-like phenomena in systems of units with two or more oscillation
modes. The model can also explain how periodic dynamics can be generated by
coupling largely stochastic units. Similar systems could be responsible for the
emergence of rhythmic behavior in complex biological or sociological systems.Comment: 4 pages, RevTex, 5 figure
Highly synchronized noise-driven oscillatory behavior of a FitzHugh-Nagumo ring with phase-repulsive coupling
We investigate a ring of FitzHugh--Nagumo elements coupled in
\emph{phase-repulsive} fashion and submitted to a (subthreshold) common
oscillatory signal and independent Gaussian white noises. This system can be
regarded as a reduced version of the one studied in [Phys. Rev. E \textbf{64},
041912 (2001)], although externally forced and submitted to noise. The
noise-sustained synchronization of the system with the external signal is
characterized.Comment: 7 pages, 15 figures, uses aipproc.cls, aip-6s.clo and aipxfm.sty.
"Cooperative Behavior in Neural Systems: Ninth Granada Lectures'', edited by
J. Marro, P. L. Garrido, and J. J. Torre
Triggering synchronized oscillations through arbitrarily weak diversity in close-to-threshold excitable media
It is shown that arbitrarily weak (frozen) heterogeneity can induce global
synchronized oscillations in excitable media close to threshold. The work is
carried out on networks of coupled van der Pol-FitzHugh-Nagumo oscillators. The
result is shown to be robust against the presence of internal dynamical noise.Comment: 4 pages (RevTeX 3 style), 5 EPS figures, submitted to Phys. Rev. E
(16 aug 2001
Wave nucleation rate in excitable systems in the low noise limit
Motivated by recent experiments on intracellular calcium dynamics, we study
the general issue of fluctuation-induced nucleation of waves in excitable
media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a
spatially-extended non-potential pair of equations driven by thermal (i.e.
white) noise. The nucleation rate is determined by finding the most probable
escape path via minimization of an action related to the deviation of the
fields from their deterministic trajectories. Our results pave the way both for
studies of more realistic models of calcium dynamics as well as of nucleation
phenomena in other non-equilibrium pattern-forming processes
Spatial Coherence Resonance near Pattern-Forming Instabilities
The analogue of temporal coherence resonance for spatial degrees of freedom
is reported. Specifically, we show that spatiotemporal noise is able to
optimally extract an intrinsic spatial scale in nonlinear media close to (but
before) a pattern-forming instability. This effect is observed in a model of
pattern-forming chemical reaction and in the Swift-Hohenberg model of fluid
convection. In the latter case, the phenomenon is described analytically via an
approximate approach.Comment: 4 pages, 4 figure
The effect of spatially correlated noise on coherence resonance in a network of excitable cells
We study the effect of spatially correlated noise on coherence resonance (CR)
in a Watts-Strogatz small-world network of Fitz Hugh-Nagumo neurons, where the
noise correlation decays exponentially with distance between neurons. It is
found that CR is considerably improved just by a small fraction of long-range
connections for an intermediate coupling strength. For other coupling
strengths, an abrupt change in CR occurs following the drastic fracture of the
clustered structures in the network. Our study shows that spatially correlated
noise plays a significant role in the phenomenon of CR through enforcing the
clustering of the network.Comment: 11 pages, 4 figur
On the role of chemical synapses in coupled neurons with noise
We examine the behavior in the presence of noise of an array of Morris-Lecar
neurons coupled via chemical synapses. Special attention is devoted to
comparing this behavior with the better known case of electrical coupling
arising via gap junctions. In particular, our numerical simulations show that
chemical synapses are more efficient than gap junctions in enhancing coherence
at an optimal noise (what is known as array-enhanced coherence resonance): in
the case of (nonlinear) chemical coupling, we observe a substantial increase in
the stochastic coherence of the system, in comparison with (linear) electrical
coupling. We interpret this qualitative difference between both types of
coupling as arising from the fact that chemical synapses only act while the
presynaptic neuron is spiking, whereas gap junctions connect the voltage of the
two neurons at all times. This leads in the electrical coupling case to larger
correlations during interspike time intervals which are detrimental to the
array-enhanced coherence effect. Finally, we report on the existence of a
system-size coherence resonance in this locally coupled system, exhibited by
the average membrane potential of the array.Comment: 7 pages, 7 figure
Dynamic Renormalization Group and Noise Induced Transitions in a Reaction Diffusion Model
We investigate how additive weak noise (correlated as well as uncorrelated)
modifies the parameters of the Gray-Scott (GS) reaction diffusion system by
performing numerical simulations and applying a Renormalization Group (RG)
analysis in the neighborhood of the spatial scale where biochemical reactions
take place. One can obtain the same sequence of spatial-temporal patterns by
means of two equivalent routes: (i) by increasing only the noise intensity and
keeping all other model parameters fixed, or (ii) keeping the noise fixed, and
adjusting certain model parameters to their running scale-dependent values as
predicted by the RG. This explicit demonstration validates the dynamic RG
transformation for finite scales in a two-dimensional stochastic model and
provides further physical insight into the coarse-graining analysis proposed by
this scheme. Through several study cases we explore the role of noise and its
temporal correlation in self-organization and propose a way to drive the system
into a new desired state in a controlled way.Comment: 8 pages, 21 figure
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