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: 25
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