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Bidirectional Conservative–Dissipative Transitions in a Five-Dimensional Fractional Chaotic System

Author

Listed:
  • Yiming Wang

    (Intelligent Manufacturing Institute, Heilongjiang Academy of Sciences, Harbin 150090, China)

  • Fengjiao Gao

    (Intelligent Manufacturing Institute, Heilongjiang Academy of Sciences, Harbin 150090, China)

  • Mingqing Zhu

    (Intelligent Manufacturing Institute, Heilongjiang Academy of Sciences, Harbin 150090, China)

Abstract

This study investigates a modified five-dimensional chaotic system by incorporating structural term adjustments and Caputo fractional-order differential operators. The modified system exhibits significantly enriched dynamic behaviors, including offset boosting, phase trajectory rotation, phase trajectory reversal, and contraction phenomena. Additionally, the system exhibits bidirectional transitions—conservative-to-dissipative transitions governed by initial conditions and dissipative-to-conservative transitions controlled by fractional order variations—along with a unique chaotic-to-quasiperiodic transition observed exclusively at low fractional orders. To validate the system’s physical realizability, a signal processing platform based on Digital Signal Processing (DSP) is implemented. Experimental measurements closely align with numerical simulations, confirming the system’s feasibility for practical applications.

Suggested Citation

  • Yiming Wang & Fengjiao Gao & Mingqing Zhu, 2025. "Bidirectional Conservative–Dissipative Transitions in a Five-Dimensional Fractional Chaotic System," Mathematics, MDPI, vol. 13(15), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2477-:d:1715124
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    1. Folifack Signing, V.R. & Gakam Tegue, G.A. & Kountchou, M. & Njitacke, Z.T. & Tsafack, N. & Nkapkop, J.D.D. & Lessouga Etoundi, C.M. & Kengne, J., 2022. "A cryptosystem based on a chameleon chaotic system and dynamic DNA coding," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Singh, Jay Prakash & Roy, Binoy Krishna, 2018. "Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 81-91.
    3. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. J.F. Gómez-Aguilar & H. Yépez-Martínez & R.F. Escobar-Jiménez & C.M. Astorga-Zaragoza & L.J. Morales-Mendoza & M. González-Lee, 2015. "Universal character of the fractional space-time electromagnetic waves in dielectric media," Journal of Electromagnetic Waves and Applications, Taylor & Francis Journals, vol. 29(6), pages 727-740, April.
    5. Zhang, Zefeng & Huang, Lilian & Liu, Jin & Guo, Qiang & Du, Xiuli, 2022. "A new method of constructing cyclic symmetric conservative chaotic systems and improved offset boosting control," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    6. Fan, Zhenyi & Zhang, Chenkai & Wang, Yiming & Du, Baoxiang, 2023. "Construction, dynamic analysis and DSP implementation of a novel 3D discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Leng, Xiangxin & Gu, Shuangquan & Peng, Qiqi & Du, Baoxiang, 2021. "Study on a four-dimensional fractional-order system with dissipative and conservative properties," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Aiguo Wu & Shijian Cang & Ruiye Zhang & Zenghui Wang & Zengqiang Chen, 2018. "Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points," Complexity, Hindawi, vol. 2018, pages 1-8, April.
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