25 research outputs found
Aspects of stochastic resonance in reaction-diffusion systems: The nonequilibrium-potential approach
We analyze several aspects of the phenomenon of stochastic resonance in
reaction-diffusion systems, exploiting the nonequilibrium potential's
framework. The generalization of this formalism (sketched in the appendix) to
extended systems is first carried out in the context of a simplified scalar
model, for which stationary patterns can be found analytically. We first show
how system-size stochastic resonance arises naturally in this framework, and
then how the phenomenon of array-enhanced stochastic resonance can be further
enhanced by letting the diffusion coefficient depend on the field. A yet less
trivial generalization is exemplified by a stylized version of the
FitzHugh-Nagumo system, a paradigm of the activator-inhibitor class. After
discussing for this system the second aspect enumerated above, we derive from
it -through an adiabatic-like elimination of the inhibitor field- an effective
scalar model that includes a nonlocal contribution. Studying the role played by
the range of the nonlocal kernel and its effect on stochastic resonance, we
find an optimal range that maximizes the system's response.Comment: 16 pages, 15 figures, uses svjour.cls and svepj-spec.clo. Minireview
to appear in The European Physical Journal Special Topics (issue in memory of
Carlos P\'erez-Garc\'{\i}a, edited by H. Mancini
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
Noise-induced phase transitions: Effects of the noises' statistics and spectrum
The local, uncorrelated multiplicative noises driving a second-order, purely
noise-induced, ordering phase transition (NIPT) were assumed to be Gaussian and
white in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. The
potential scientific and technological interest of this phenomenon calls for a
study of the effects of the noises' statistics and spectrum. This task is
facilitated if these noises are dynamically generated by means of stochastic
differential equations (SDE) driven by white noises. One such case is that of
Ornstein--Uhlenbeck noises which are stationary, with Gaussian pdf and a
variance reduced by the self-correlation time (\tau), and whose effect on the
NIPT phase diagram has been studied some time ago. Another such case is when
the stationary pdf is a (colored) Tsallis' (q)--\emph{Gaussian} which, being a
\emph{fat-tail} distribution for (q>1) and a \emph{compact-support} one for
(q<1), allows for a controlled exploration of the effects of the departure from
Gaussian statistics. As done before with stochastic resonance and other
phenomena, we now exploit this tool to study--within a simple mean-field
approximation and with an emphasis on the \emph{order parameter} and the
``\emph{susceptibility}''--the combined effect on NIPT of the noises'
statistics and spectrum. Even for relatively small (\tau), it is shown that
whereas fat-tail noise distributions ((q>1)) counteract the effect of
self-correlation, compact-support ones ((q<1)) enhance it. Also, an interesting
effect on the susceptibility is seen in the last case.Comment: 6 pages, 10 figures, uses aipproc.cls, aip-8s.clo and aipxfm.sty. To
appear in AIP Conference Proceedings. Invited talk at MEDYFINOL'06 (XV
Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics
Invited review: KPZ. Recent developments via a variational formulation
Recently, a variational approach has been introduced for the paradigmatic
Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together
with the functional Taylor expansion that the KPZ nonequilibrium potential
(NEP) admits. Such expansion becomes naturally truncated at third order, giving
rise to a nonlinear stochastic partial differential equation to be regarded as
a gradient-flow counterpart to the KPZ equation. A dynamic renormalization
group analysis at one-loop order of this new mesoscopic model yields the KPZ
scaling relation alpha+z=2, as a consequence of the exact cancelation of the
different contributions to vertex renormalization. This result is quite
remarkable, considering the lower degree of symmetry of this equation, which is
in particular not Galilean invariant. In addition, this scheme is exploited to
inquire about the dynamical behavior of the KPZ equation through a
path-integral approach. Each of these aspects offers novel points of view and
sheds light on particular aspects of the dynamics of the KPZ equation.Comment: 16 pages, 2 figure
Nonequilibrium phase transitions induced by multiplicative noise: effects of self-correlation
A recently introduced lattice model, describing an extended system which
exhibits a reentrant (symmetry-breaking, second-order) noise-induced
nonequilibrium phase transition, is studied under the assumption that the
multiplicative noise leading to the transition is colored. Within an effective
Markovian approximation and a mean-field scheme it is found that when the
self-correlation time of the noise is different from zero, the transition is
also reentrant with respect to the spatial coupling D. In other words, at
variance with what one expects for equilibrium phase transitions, a large
enough value of D favors disorder. Moreover, except for a small region in the
parameter subspace determined by the noise intensity and D, an increase in the
self-correlation time usually preventsthe formation of an ordered state. These
effects are supported by numerical simulations.Comment: 15 pages. 9 figures. To appear in Phys.Rev.
Wide-spectrum energy harvesting out of colored LĂ©vy-like fluctuations, by monostable piezoelectric transducers
This work aims to optimize the overall performance of a model oscillator, as an energy harvester of LĂ©vy-like mesoscopic fluctuations through piezoelectric conversion. As a further step in the description of a realistic harvesting device we consider a monostable Woods-Saxon oscillator, which can interpolate between square well and harmonic-like behaviors. We study the interplay between the potential shape and the noise's spectrum and statistics. The dependence of the power output on the parameters determining those features indicates the directions in which the former can be increased
Nonequilibrium phase transitions induced by multiplicative noise: Effects of self-correlation
A recently introduced lattice model, describing an extended system which exhibits a reentrant (symmetry-breaking, second-order) noise-induced nonequilibrium phase transition, is studied under the assumption that the multiplicative noise leading to the transition is colored. Within an effective Markovian approximation and a mean-field scheme it is found that when the self-correlation time Ï of the noise is different from zero, the transition is also reentrant with respect to the spatial coupling D. In other words, at variance with what one expects for equilibrium phase transitions, a large enough value of D favors disorder. Moreover, except for a small region in the parameter subspace determined by the noise intensity Ï and D, an increase in Ï usually prevents the formation of an ordered state. These effects are supported by numerical simulations.R. T. acknowledges ïŹnancial support from DGICyT, project numbers PB94-1167 and PB97- 0141-C02-01. H. S. W, R. R. D. and S. E. M. acknowledge ïŹnancial support from CONICET, project number PIP-4953/96, and from ANPCyT, project number .Peer Reviewe
A Nonequilibrium-Potential Approach to Competition in Neural Populations
Energy landscapes are a highly useful aid for the understanding of dynamical systems, and a particularly valuable tool for their analysis. For a broad class of rate neural-network models of relevance in neuroscience, we derive a global Lyapunov function which provides an energy landscape without any symmetry constraint. This newly obtained ânonequilibrium potentialâ (NEP)âthe first one obtained for a model of neural circuitsâpredicts with high accuracy the outcomes of the dynamics in the globally stable cases studied here. Common features of the models in this class are bistabilityâwith implications for working memory and slow neural oscillationsâand population bursts, associated with signal detection in neuroscience. Instead, limit cycles are not found for the conditions in which the NEP is defined. Their nonexistence can be proven by resorting to the BendixsonâDulac theorem, at least when the NEP remains positive and in the (also generic) singular limit of these models. This NEP constitutes a powerful tool to understand average neural network dynamics from a more formal standpoint, and will also be of help in the description of large heterogeneous neural networks.RD acknowledges support from UNMdP http://dx.doi.org/10.13039/501100007070, under Grant 15/E779âEXA826/17. NM acknowledges a Doctoral Fellowship from CONICET http://dx.doi.org/10.13039/501100002923.Peer reviewe