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journal contributionposted on 2023-05-18, 00:04 authored by Robert DelbourgoRobert Delbourgo, Kenny, BG
By analyzing the functional equations governing N replication for real nonlinear maps on the (unit) interval (of order z), we have derived the asymptotic (N-->∞) behaviors of the scaling constants alpha and delta, alpha(z)~(2z)(N-1)/(z-1), delta/alphaz=(z-1)/(z-1/2). In addition, we have determined the limiting forms of the universal functions. The predictions are in excellent agreement with (separately compiled) numerical data over a wide range of z values and cycle structures.
Publication titlePhysical Review A
Department/SchoolSchool of Natural Sciences
PublisherAmerican Physical Soc
Place of publicationOne Physics Ellipse, College Pk, USA, Md, 20740-3844