Structure formation in a conserved mass model of a set of individuals interacting with attractive and repulsive forces.

We study a set of interacting individuals that conserve their total mass. In order to describe its dynamics we resort to mesoscopic equations of reaction diffusion including currents driven by attractive and repulsive forces. For the mass conservation we consider a linear response parameter that maintains the mass in the vicinity of a optimal value which is determined by the set. We use the reach and intensity of repulsive forces as control parameters. When sweeping a wide range of parameter space we find a great diversity of localized structures, stationary as well as other ones with cyclical and chaotic dynamics. We compare our results with real situations.

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. The numerical results are supported by an analytical estimate in the spirit of the so-called solvability condition.

Cooperation between fluctuations and spatial coupling for two symmetry breakings in a gradient system.

A zero-dimensional system that is affected by field-dependent fluctuations evolves toward the field's values in which the fluctuations' effect is minimized. For a high enough noise intensity, it causes an exchange of roles between the stable and unstable state. In this paper, we report symmetry breaking in two stable states, but one of them stabilized by the fluctuations while exchanging its role with a previously stable state.

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.

Interplay between noise and boundary conditions in pattern formation in adsorbed substances.

We have studied the interplay between noise and boundary conditions on the possibility of noise induced pattern formation. With this aim, we have exploited a deterministic model for pattern formation in adsorbed substances--including the effect of lateral interactions--used to describe the phenomenon of adsorption in surfaces, where a multiplicative noise fulfilling a fluctuation-dissipation relation was added. We have found solutions for different boundary conditions, particularly corresponding to two stable and one unstable patterns, where one of the stable and the unstable one, are purely induced by the multiplicative noise. In the case of albedo boundary conditions we have found a transition from monostable to a noise induced bistable behavior as the albedo parameter is varied.