We studied the effect of nearest pattern interaction on a global pattern formation in a two-dimensional space, where patterns are to grow initially from a noise in the presence of a periodic supply of energy. Although our approach is general, we found that this study is relevant in particular to the pattern formation on a periodically vibrated granular layer, as it gives a unified perspective o...

The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics term, accounting for the local rate of variation of the field variable, (ii) a noise component (additive or multiplicative) accounting for the unavoidable env...

Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. Possible mechanisms include oscillating consumer-resource interactions, localized disturbance-recovery processes and scale-dependent feedback. Despite abundant theoretical literature, studies revealing spatial self-organization in real ecosystems are limited. Rec...

Naturally, deformed rocks commonly contain crack arrays (joints) forming patterns with systematic relationships to the large-scale deformation. Kinematically, joints can be mode-1, -2 or -3 or combinations of these, but there is no overarching theory for the development of the patterns. We develop a model motivated by dislocation pattern formation in metals. The problem is formulated in one dim...

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation ...

We analyze pattern formation in doubly resonant intracavity second-harmonic generation in the presence of competing nondegenerate parametric downconversion. We show that for positive cavity detuning of the fundamental frequency the threshold for parametric oscillation is lower than that of transverse, pattern forming instabilities. The parametric oscillation strongly modifies the pattern dynami...