Collision of Feigenbaum cascades

Year: 1984

Authors: Oppo G.L., Politi A.

Autors Affiliation: Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy

Abstract: The existence in dynamical systems of chaotic bands delimited on both sides by period-doubling cascades is a general two-parameter phenomenon. Evidence is presented to show that, whenever these chaotic regions disappear, the bifurcation convergence rate undergoes a slowing down and asymptotically approaches the square root of the universal number delta = approximately 4.6692. A simple renormalization-group analysis is performed to explain this critical behavior and its scaling properties. In particular a theoretical universal function describing the evolution of the convergence rate from sq rt delta to delta is given and numerically verified.

Journal/Review: PHYSICAL REVIEW A

Volume: 30 (1)      Pages from: 435  to: 441

KeyWords: nonlinear systems; stocastic processes;
DOI: 10.1103/PhysRevA.30.435

Citations: 26
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-17
References taken from IsiWeb of Knowledge: (subscribers only)
Connecting to view paper tab on IsiWeb: Click here
Connecting to view citations from IsiWeb: Click here