title: Adaptation to the edge of chaos with random-wavelet feedback.
abstract: We studied the effect of low-pass band filters on the dynamics of a nonisothermal autocatalator as seen through feedback on a system parameter. Filters were created by selecting Fourier coefficients for the modes in the pass band according to a uniform distribution. Numerical simulations over many realizations of feedback were compared to theoretical predictions for the feedback size as a function of the parameter. We found that the variance in the feedback was nonzero only near and within chaotic regimes in the parameter space. We numerically calculated the probability density for the parameter, showing that the system adapts to the edge of chaos.
authors.affiliation: Center for Complex Systems Research, Physics Department, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA. wothersp@uiuc.edu
authors.forename: Timothy
authors.initials: T
authors.lastname: Wotherspoon
authors.forename: Alfred
authors.initials: A
authors.lastname: Hübler