Route to Chaos in Three-Dimensional Maps of Logistic Type
Chaotic Dynamics
2007-05-23 v1 Dynamical Systems
Pattern Formation and Solitons
Populations and Evolution
Abstract
A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the 2-dimensional case. When the parameter of the system is modified, localized oscillations occur on the ICC that give rise to weakly chaotic rings, then to chaotic attractors, which finally disappear by contact bifurcations. These maps can be considered as models for the symbiotic interaction of three species.
Cite
@article{arxiv.nlin/0502012,
title = {Route to Chaos in Three-Dimensional Maps of Logistic Type},
author = {Daniele Fournier-Prunaret and Ricardo Lopez-Ruiz and Abdel-Kaddous Taha},
journal= {arXiv preprint arXiv:nlin/0502012},
year = {2007}
}
Comments
8 pages, 15 figures