Universal shape law of stochastic supercritical bifurcations: Theory and experiments

Details Universal shape law of stochastic supercritical bifurcations: Theory and experiments Universal shape law of stochastic supercritical bifurcations: Theory and experiments

2007-02-28

arxiv.org/abs/nlin/0702057v1

Nonlinear Sciences

Pattern Formation and Solitons

5 pages, 5 figures

Scientific paper

10.1103/PhysRevE.77.026218

A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading to the expression for the most probable amplitude of the critical mode. From this universal expression, the shape of the bifurcation, its location and its evolution with the noise level are completely defined. Experimental results obtained for a 1D transverse Kerr-like slice subjected to optical feedback are in excellent agreement.

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