Characterizing the information transmission of inverse stochastic resonance and noise-induced activity amplification in neuronal systems.

Purkinje cells exhibit a reduction of the mean firing rate at intermediate-noise intensities, which is somewhat reminiscent of the response enhancement known as "stochastic resonance" (SR). Although the comparison with the stochastic resonance ends here, the current phenomenon has been given the name "inverse stochastic resonance" (ISR). Recent research has demonstrated that the ISR effect, like its close relative "nonstandard SR" [or, more correctly, noise-induced activity amplification (NIAA)], has been shown to stem from the weak-noise quenching of the initial distribution, in bistable regimes where the metastable state has a larger attraction basin than the global minimum.

Limiting the stroke of a Schmitt trigger with multiplicative noise.

We have devised an experiment whereby a bistable system is confined away from its deterministic attractors by means of multiplicative noise. Together with previous numerical results, our experimental results validate the hypothesis that the higher the slope of the noise's multiplicative factor, the more it shifts the stationary states.

Stochastic dissipative solitons.

By the effect of aggregating currents, some systems display an effective diffusion coefficient that becomes negative in a range of the order parameter, giving rise to bistability among homogeneous states (HSs). By applying a proper multiplicative noise, localized (pinning) states are shown to become stable at the expense of one of the HSs. They are, however, not static, but their location fluctuates with a variance that increases with the noise intensity.

Nonequilibrium pattern formation by subdominant attractive forces: a simple model and a stabilization strategy by means of noise.

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.

Recent developments on the Kardar-Parisi-Zhang surface-growth equation.

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 people to adopt it as a 'standard' model in the field during the last quarter of a century. At the same time, several conjectures deserving closer scrutiny were established as dogmas throughout the community.

Modular system for data acquisition and control of experiments with digital output.

In the present work, the design of an efficient, modular, and scalable data acquisition and control system is described. It consists of an array of microcontrollers and memories, which feed a single concentrating unit whose information can be accessed by means of a universal series bus (USB) interface to be processed later on. Signal levels can be controlled through a set of digital potentiometers.

Discretization-related issues in the Kardar-Parisi-Zhang equation: consistency, Galilean-invariance violation, and fluctuation-dissipation relation.

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 arbitrariness in the choice of spatial discretization schemes. On one hand, the discretization prescriptions for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen.

Replication of noise-sustained autocatalytic chemical structures.

Autocatalytic systems in a differential-flow reactor may undergo a differential-flow-induced chemical instability toward a convectively unstable regime, in which noise-sustained structures may appear. This is the case of a system with Gray-Scott kinetics in a packed-bed reactor, as reported in [B. von Haeften and G.

Anomalous nonequilibrium Ising-Bloch bifurcation in discrete systems.

We investigate the self-organization of two-dimensional activator-inhibitor discrete bistable systems in the neighborhood of a nonequilibrium Ising-Bloch bifurcation. The system exhibits an anomalous transition--induced by discretization--whose signature is the coexistence of Ising and Bloch walls for selected values of the spatial coupling. After curvature reduction of Bloch walls, coexistence gives rise to a unique and striking spatiotemporal dynamics: Bloch walls drive the motion and Ising walls play the role of "extended defects" oriented along the background grid directions.

Coupling-reentrant phase transition, complex hysteretic behavior, and efficiency optimization in coupled phase oscillators submitted to colored flashing potentials.

A recent mean-field analysis of a model consisting of N nonlinear phase oscillators-under the joint influence of global periodic coupling with strength K0 and of local multiplicative and additive noises-has shown a nonequilibrium phase transition towards a broken-symmetry phase exhibiting noise-induced transport, or "ratchet" behavior. In a previous paper we focused on the relationship between the character of the (mean velocity vs load force F) hysteresis loop, the number of "homogeneous" mean-field solutions, and the shape of the stationary mean-field probability distribution function (PDF). Here we assume that the multiplicative noises of the model are Ornstein-Uhlenbeck with common strength Q and self-correlation time tau.

Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean-field approach.

We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchetlike transport mechanism arises through a symmetry-breaking noise-induced nonequilibrium phase transition. Numerical simulations of this system reveal amazing novel features such as negative zero-bias conductance and anomalous hysteresis, explained by performing a strong-coupling analysis in the thermodynamic limit. Using an explicit mean-field approximation, we explore the whole ordered phase finding a transition from anomalous to normal hysteresis inside this phase, estimating its locus, and identifying (within this scheme) a mechanism whereby it takes place.

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 tau 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.