A novel delayed exponent coupled chaotic map with countering dynamical degradation

Bowen Zhang; Lingfeng Liu; Bowen Zhang; Lingfeng Liu

doi:10.3934/math.2024007

AIMS Mathematics

2024, Volume 9, Issue 1: 99-121. doi: 10.3934/math.2024007

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Research article

A novel delayed exponent coupled chaotic map with countering dynamical degradation

Bowen Zhang ,
Lingfeng Liu ^,

School of Software, Nanchang University, Nanchang 330031, China

Received: 08 October 2023 Revised: 14 November 2023 Accepted: 21 November 2023 Published: 27 November 2023
MSC : 34H10, 37G15

While chaotic systems have found extensive applications across diverse scientific domains due to their inherent advantages, they often degrade into cyclic patterns when simulated on hardware with limited computational precision. This results in a pronounced decline in properties related to chaotic dynamics. To address this issue, we introduce the delayed exponent coupled chaotic map (DECCM). This model is designed to enhance the chaotic dynamics of the original map, especially at lower computational precisions. Additionally, DECCM can transform any proficient 1-dimensional seed map into an N-dimensional chaotic map. Extensive simulation and performance tests attest to the robust chaotic characteristics of our approach. Furthermore, DECCM holds distinct advantages over premier algorithms, particularly in period analysis experiments. We also introduce various seed maps into DECCM to present 2D and 3D examples, ensuring their generalization through relevant performance evaluations.
- chaos,
- chaotic map,
- digital chaotic map,
- dynamical degradation,
- coupled mapping
Citation: Bowen Zhang, Lingfeng Liu. A novel delayed exponent coupled chaotic map with countering dynamical degradation[J]. AIMS Mathematics, 2024, 9(1): 99-121. doi: 10.3934/math.2024007

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Abstract

While chaotic systems have found extensive applications across diverse scientific domains due to their inherent advantages, they often degrade into cyclic patterns when simulated on hardware with limited computational precision. This results in a pronounced decline in properties related to chaotic dynamics. To address this issue, we introduce the delayed exponent coupled chaotic map (DECCM). This model is designed to enhance the chaotic dynamics of the original map, especially at lower computational precisions. Additionally, DECCM can transform any proficient 1-dimensional seed map into an N-dimensional chaotic map. Extensive simulation and performance tests attest to the robust chaotic characteristics of our approach. Furthermore, DECCM holds distinct advantages over premier algorithms, particularly in period analysis experiments. We also introduce various seed maps into DECCM to present 2D and 3D examples, ensuring their generalization through relevant performance evaluations.

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