Parametric evolution of unstable dimension variability in coupled piecewise-linear chaotic maps
Abstract
In presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one step further in obtaining such results, we study the parametric evolution of unstable dimension variability in two coupled bungalow maps. Each of these maps presents intervals of linearity that define Markov partitions, which are recovered for the coupled system in the case of synchronization. Using such partitions we find exact results for the onset of unstable dimension variability and for contrast measure, which quantifies the intensity of the phenomenon in terms of the stability of the periodic orbits embedded in the synchronization subspace.
Cite
@article{arxiv.1011.6003,
title = {Parametric evolution of unstable dimension variability in coupled piecewise-linear chaotic maps},
author = {Rodrigo Frehse Pereira and Marcos C. Verges and Ricardo L. Viana and Sergio R. Lopes and Sandro Ely de Souza Pinto},
journal= {arXiv preprint arXiv:1011.6003},
year = {2010}
}
Comments
5 pages, 2 figures - to be submitted to Physical Review E - Brief Report