Noise and dynamic transitions

1997/07/31 by Grant Lythe, Lythe, G. D.
Decision Sciences · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Probabilistic and Robust Engineering Design #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.adap-org/9707007

openalex publication_date 1997/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A parabolic stochastic PDE is studied analytically and numerically, when a bifurcation parameter is slowly increased through its critical value. The aim is to understand the effect of noise on delayed bifurcations in systems with spatial degrees of freedom. Realisations of the nonautonomous stochastic PDE remain near the unstable configuration for a long time after the bifurcation parameter passes through its critical value, then jump to a new configuration. The effect of the nonlinearity is to freeze in the spatial structure formed from the noise near the critical value.

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