title: Adaptation to the edge of chaos in the self-adjusting logistic map.
abstract: 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.
authors.affiliation: Center for Complex Systems Research, Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA.
authors.forename: P
authors.initials: P
authors.lastname: Melby
authors.forename: J
authors.initials: J
authors.lastname: Kaidel
authors.forename: N
authors.initials: N
authors.lastname: Weber
authors.forename: A
authors.initials: A
authors.lastname: Hübler
mesh_terms: D000220:Adaptation, Biological; D000818:Animals; D001517:Coleoptera; D004777:Environment; D005246:Feedback; D005583:Fourier Analysis; D016015:Logistic Models; D008432:Mathematical Computing; D008954:Models, Biological; D017711:Nonlinear Dynamics