Agez Gonzague, Clerc Marcel G, Louvergneaux Eric, Rojas René G
Centre d'Elaboration de Matériaux et d'Etudes Structurales, Université Paul Sabatier, 29, rue Jeanne Marvig, BP 94347, 31055 Toulouse Cedex 4, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):042919. doi: 10.1103/PhysRevE.87.042919. Epub 2013 Apr 23.
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.
从理论、数值和实验方面研究了加性噪声对一维系统中超临界和亚临界空间分岔影响的通用描述。推导了临界空间模式振幅的概率密度。根据这种广义瑞利分布，我们通过临界模式振幅的最概然值预测噪声分岔的形状。对于描述随机超临界分岔的三次或五次振幅方程以及描述随机亚临界分岔的三次 - 五次振幅方程，与数值模拟的比较结果吻合得相当好。在受光反馈作用的一维类克尔切片中获得的实验结果证实了超临界分岔形状的解析表达式预测。
