Dynamics controlled by additive noise

1997/08/11 by Grant Lythe, Lythe, G. D.
Computer Science · Neuroscience · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.adap-org/9708005

openalex publication_date 1997/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows small random disturbances to exert a controlling influence. A map is derived which provides an accurate description of the trajectories.

Citations

• Pattern formation outside of equilibrium

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