Collision of Feigenbaum cascades
Abstract
The existence in dynamical systems of chaotic bands delimited on both sides by perioddoubling cascades is a general twoparameter phenomenon. Here we show evidence that, whenever these chaotic regions disappear, the bifurcation convergence rate undergoes a slowing down and asymptotically approaches the square root of the universal number δ=4.6692.... A simple renormalizationgroup 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 δ^{12}, to δ is given and numerically verified.
 Publication:

Physical Review A
 Pub Date:
 July 1984
 DOI:
 10.1103/PhysRevA.30.435
 Bibcode:
 1984PhRvA..30..435O
 Keywords:

 Nonlinear Systems;
 Stochastic Processes;
 Theoretical Physics;
 Branching (Mathematics);
 Condensates;
 Convergence;
 Period Doubling;
 Phase Transformations;
 Physics (General)