Dynamics of self-adjusting systems with noise

Paul Melby, Nicholas Weber, Alfred Hübler

Research output: Contribution to journalArticlepeer-review


We study several self-adjusting systems with noise. In our analytical and numerical studies, we find that the dynamics of the self-adjusting parameter can be accurately described with a rescaled diffusion equation. We find that adaptation to the edge of chaos, a feature previously ascribed to self-adjusting systems, is only a long-lived transient when noise is present in the system. In addition, using analytical, numerical, and experimental methods, we find that noise can cause chaotic outbreaks where the parameter reenters the chaotic regime and the system dynamics become chaotic. We find that these chaotic outbreaks have a power law distribution in length.

Original languageEnglish (US)
Article number033902
Issue number3
StatePublished - Sep 2005

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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