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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.(More)
A recently introduced lattice model, describing an extended system which exhibits a reentrant ~symmetrybreaking, 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(More)
The stochastic nonlinear partial differential equation known as the Kardar-Parisi-Zhang (KPZ) equation is a highly successful phenomenological mesoscopic model of surface and interface growth processes. Its suitability for analytical work, its explicit symmetries and its prediction of an exact dynamic scaling relation for a one-dimensional substratum led(More)
Numerical evidence is presented of a coherence-resonant behavior, induced on an atmospheric global circulation model by a white (in time and space) additive Gaussian noise with amplitude A << 1 . Intermediate A values enhance the spatiotemporal regularity of vortical patterns that contribute to the intra-annual variability of the atmospheric component of(More)
Strong constraints are drawn for the choice of real-space discretization schemes, using the known fact that the KPZ equation results from a diffusion equation (with multiplicative noise) through a Hopf–Cole transformation. Whereas the nearest-neighbor discretization passes the consistency tests, known examples in the literature do not. We emphasize the(More)
In order to perform numerical simulations of the Kardar-Parisi-Zhang (KPZ) equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf-Cole transformation applied to a diffusion equation (with multiplicative noise) is shown here to strongly restrict the(More)
As a mock-up of synaptic transmission between neurons, we revisit a problem that has recently risen the interest of several authors: the propagation of a low-frequency periodic signal through a chain of one-way coupled bistable oscillators, subject to uncorrelated additive noise. On a numerical study performed in the optimal range of noise intensity for(More)
(1) Instituto de F́ısica de Cantabria (UC and CSIC), Avda. de los Castros, s/n, E-39005 Santander, Spain; (2) ICMAT (CSIC-UAM-UC3M-UCM), Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain; (3) Instituto de Investigaciones F́ısicas Mar del Plata (UNMdP and CONICET), Deán(More)
We introduce a simple model describing a mechanism for transient pattern formation driven by subdominant attractive forces. The patterns can be stabilized if they are confined by means of a particular multiplicative noise into the region where such mechanism is active. The scope of the results appears to transcend the original application context.
Two identical 1D autocatalytic systems with Gray–Scott kinetics—driven towards convectively unstable regimes and submitted to independent spatiotemporal Gaussian white noises—are coupled unidirectionally, but otherwise linearly. Numerical simulation then reveals that (even when perturbed by noise) the slave system replicates the convective patterns arising(More)