title: Dynamics of self-adjusting systems with noise.
abstract: 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.
authors.affiliation: Center for Complex Systems Research, Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA. paulmelby@gmail.com
authors.forename: Paul
authors.initials: P
authors.lastname: Melby
authors.forename: Nicholas
authors.initials: N
authors.lastname: Weber
authors.forename: Alfred
authors.initials: A
authors.lastname: Hübler
mesh_terms: D000222:Adaptation, Physiological / Q000502:physiology*; D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D013269:Stochastic Processes