Adaptation to the edge of chaos in the self-adjusting logistic map

Paul Melby, Jörg Kaidel, Nicholas Weber, Alfred Hübler

Research output: Contribution to journalArticlepeer-review


Self-adjusting, or adaptive, systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dynamical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter leaves the chaotic regime. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.

Original languageEnglish (US)
Pages (from-to)5991-5993
Number of pages3
JournalPhysical review letters
Issue number26
StatePublished - 2000
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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