# Entropy Map Might Be Chaotic

### Junping Hong, Wai Chan

#### Abstract

Chaos is a phenomenon observable in many areas. Chaotic behaviours can be visualized in chaotic maps, which are deterministic iterative functions and sensitive to initial conditions. As a result, they are wildly adopted in random number generator, image encryption, etc. In this paper, two new chaotic maps inspired by information entropy are proposed. Through bifurcation diagram and Lyapunov exponent analysis, period doubling bifurcations are observed and chaos is suggested. Furthermore, these maps lead to a special case of the Frobenius-Perron operator in their distributions and are extended to the complex plane to obtain the Julia set.

Download#### Paper Citation

#### in Harvard Style

Hong J. and Chan W. (2021). **Entropy Map Might Be Chaotic**. In *Proceedings of the 6th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,* ISBN 978-989-758-505-0, pages 86-90. DOI: 10.5220/0010469700860090

#### in Bibtex Style

@conference{complexis21,

author={Junping Hong and Wai Chan},

title={Entropy Map Might Be Chaotic},

booktitle={Proceedings of the 6th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,},

year={2021},

pages={86-90},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010469700860090},

isbn={978-989-758-505-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,

TI - Entropy Map Might Be Chaotic

SN - 978-989-758-505-0

AU - Hong J.

AU - Chan W.

PY - 2021

SP - 86

EP - 90

DO - 10.5220/0010469700860090