Chaotic dynamics analysis and control of fractional-order ESER systems using a high-precision Caputo derivative approach

XiongFei Chi; Ting Wang; ZhiYuan Li; XiongFei Chi; Ting Wang; ZhiYuan Li

doi:10.3934/era.2025161

Electronic Research Archive

2025, Volume 33, Issue 6: 3613-3637. doi: 10.3934/era.2025161

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Research article

Chaotic dynamics analysis and control of fractional-order ESER systems using a high-precision Caputo derivative approach

1.
Department of Mechanical and Electrical Engineering, Ordos Vocational College, Ordos 017010, China
2.
College of Date Science and Application, Inner Mongolia University of Technology, Hohhot 010080, China

Received: 02 May 2025 Revised: 30 May 2025 Accepted: 06 June 2025 Published: 11 June 2025

This paper investigates the chaotic dynamics and control of a fractional-order energy-saving and emission-reduction (ESER) system using a high-precision method. By constructing a four-dimensional fractional-order system, the complex interactions between new energy, carbon emissions, economic growth, and carbon trading volume are studied. A novel high-precision numerical method, based on generating functions, is introduced to analyze the dynamic behaviors of the system at various fractional derivatives and parameters. Numerical simulations find all kinds of dynamic behaviors, including stable, rapid divergence, and chaotic attractors. In this study, we design feedback and adaptive control strategies to achieve chaos synchronization and system stability. The results highlight the effectiveness of the proposed control methods in stabilizing the system and synchronizing drive-response systems, underscoring the pivotal role of fractional-order derivatives in regulating system dynamics.
- dynamics analysis,
- fractional-order system,
- chaotic control,
- high-precision method,
- Caputo derivative,
- ESER system
Citation: XiongFei Chi, Ting Wang, ZhiYuan Li. Chaotic dynamics analysis and control of fractional-order ESER systems using a high-precision Caputo derivative approach[J]. Electronic Research Archive, 2025, 33(6): 3613-3637. doi: 10.3934/era.2025161

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Abstract

This paper investigates the chaotic dynamics and control of a fractional-order energy-saving and emission-reduction (ESER) system using a high-precision method. By constructing a four-dimensional fractional-order system, the complex interactions between new energy, carbon emissions, economic growth, and carbon trading volume are studied. A novel high-precision numerical method, based on generating functions, is introduced to analyze the dynamic behaviors of the system at various fractional derivatives and parameters. Numerical simulations find all kinds of dynamic behaviors, including stable, rapid divergence, and chaotic attractors. In this study, we design feedback and adaptive control strategies to achieve chaos synchronization and system stability. The results highlight the effectiveness of the proposed control methods in stabilizing the system and synchronizing drive-response systems, underscoring the pivotal role of fractional-order derivatives in regulating system dynamics.

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