One-dimensional Dynamics for a Discontinuous Singular Map and the Routes to Chaos

We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points. In particular, routes to chaos exist that do not exhibit pe...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-12
Main Author: Alexanian, Moorad
Format: Article
Language:English
Subjects:
Parameters
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points. In particular, routes to chaos exist that do not exhibit period-doubling whereas period-doubling is the sole route to chaos in the logistic map. Aperiodic maps are found that lead to cobwebs with x = infinity as accumulation points, where every neighborhood contains infinitely many points generated by the map.
ISSN:2331-8422
DOI:10.48550/arxiv.2212.12033