Entropy Map Might Be Chaotic

Junping Hong; Wai Kin (Victor) Chan

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Paper

Entropy Map Might Be Chaotic

Topics: Chaos Theory and Applications

In Proceedings of the 6th International Conference on Complexity, Future Information Systems and Risk COMPLEXIS - Volume 1, 86-90, 2021

Authors: Junping Hong and Wai Kin (Victor) Chan

Affiliation: Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen, China

Keyword(s): Chaos, Chaotic Map, Information Entropy, Julia Set, Frobenius-Perron Operator.

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.

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Paper citation in several formats:

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 - COMPLEXIS; ISBN 978-989-758-505-0; ISSN 2184-5034, SciTePress, pages 86-90. DOI: 10.5220/0010469700860090

@conference{complexis21,
author={Junping Hong. and Wai Kin (Victor) Chan.},
title={Entropy Map Might Be Chaotic},
booktitle={Proceedings of the 6th International Conference on Complexity, Future Information Systems and Risk - COMPLEXIS},
year={2021},
pages={86-90},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010469700860090},
isbn={978-989-758-505-0},
issn={2184-5034},
}

TY - CONF

JO - Proceedings of the 6th International Conference on Complexity, Future Information Systems and Risk - COMPLEXIS
TI - Entropy Map Might Be Chaotic
SN - 978-989-758-505-0
IS - 2184-5034
AU - Hong, J.
AU - Chan, W.
PY - 2021
SP - 86
EP - 90
DO - 10.5220/0010469700860090
PB - SciTePress