Bifurcations of emerging patterns in the presence of additive noise

被引：24

作者：

Agez, Gonzague ^{[1
]}

Clerc, Marcel G. ^{[2
]}

Louvergneaux, Eric ^{[3
]}

Rojas, Rene G. ^{[4
]}

机构：

[1] Univ Toulouse 3, Ctr Elaborat Mat & Etud Struct, F-31055 Toulouse 4, France

[2] Univ Chile, Fac Ciencias Fis & Matemat, Dept Fis, Santiago, Chile

[3] Univ Lille 1, Ctr Etud & Rech Lasers & Applicat, Lab Phys Lasers Atomes & Mol, CNRS,UMR 8523, F-59655 Villeneuve Dascq, France

[4] Pontificia Univ Catolica Valparaiso, Inst Fis, Valparaiso, Chile

来源：

PHYSICAL REVIEW E | 2013年 / 87卷 / 04期

关键词：

TRANSITION;

D O I：

10.1103/PhysRevE.87.042919

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

A universal description of the effects of additive noise on super- and subcritical spatial bifurcations in one-dimensional systems is theoretically, numerically, and experimentally studied. The probability density of the critical spatial mode amplitude is derived. From this generalized Rayleigh distribution we predict the shape of noisy bifurcations by means of the most probable value of the critical mode amplitude. Comparisons with numerical simulations are in quite good agreement for cubic or quintic amplitude equations accounting for stochastic supercritical bifurcation and for cubic-quintic amplitude equation accounting for stochastic subcritical bifurcation. Experimental results obtained in a one-dimensional Kerr-like slice subjected to optical feedback confirm the analytical expression prediction for the supercritical bifurcation shape. DOI: 10.1103/PhysRevE.87.042919

引用

页数：10

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