IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v145y2021ics0960077921001430.html
   My bibliography  Save this article

A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation

Author

Listed:
  • Liu, Tianming
  • Yan, Huizhen
  • Banerjee, Santo
  • Mou, Jun

Abstract

The definition of fractional calculus is introduced into a 3D multi-attribute chaotic system in this paper. The fractional multi-attribute chaotic system (FMACS) numerical solution is obtained based on the Adomian decomposition method (ADM). The balance points and dynamical behaviors of self-excited and hidden attractors in FMACS are compared and analyzed through the Lyapunov spectrum, bifurcation model, and complexity. It is worth noting that some hidden coexistence attractors with different shapes are affected by the order. Besides, a novel chaotic system without equilibrium points is constructed, in which the nonlinear function term in FMACS is replaced with a rare nonlinear function ex. Meanwhile, its degradation phenomenon and state transition phenomenon are analyzed in detail. Finally, the digital circuit of the system is realized on the DSP board. The research result shows that FMACS has richer dynamical behaviors and higher complexity. This research provides a theoretical basis and guidance for the application of fractional chaotic systems.

Suggested Citation

  • Liu, Tianming & Yan, Huizhen & Banerjee, Santo & Mou, Jun, 2021. "A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001430
    DOI: 10.1016/j.chaos.2021.110791
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921001430
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110791?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mezatio, Brice Anicet & Motchongom, Marceline Tingue & Wafo Tekam, Blaise Raoul & Kengne, Romanic & Tchitnga, Robert & Fomethe, Anaclet, 2019. "A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 100-115.
    2. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.
    3. Hashemi, M.S. & Inc, Mustafa & Yusuf, Abdullahi, 2020. "On three-dimensional variable order time fractional chaotic system with nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Wang, Mengjiao & Liao, Xiaohan & Deng, Yong & Li, Zhijun & Su, Yongxin & Zeng, Yicheng, 2020. "Dynamics, synchronization and circuit implementation of a simple fractional-order chaotic system with hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    5. Zhang, Yunzhen & Liu, Zhong & Wu, Huagan & Chen, Shengyao & Bao, Bocheng, 2019. "Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 354-363.
    6. Jia, Hongyan & Shi, Wenxin & Wang, Lei & Qi, Guoyuan, 2020. "Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. Jun Mou & Kehui Sun & Huihai Wang & Jingya Ruan, 2017. "Characteristic Analysis of Fractional-Order 4D Hyperchaotic Memristive Circuit," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-13, July.
    8. Fei Yu & Li Liu & Hui Shen & Zinan Zhang & Yuanyuan Huang & Changqiong Shi & Shuo Cai & Xianming Wu & Sichun Du & Qiuzhen Wan, 2020. "Dynamic Analysis, Circuit Design, and Synchronization of a Novel 6D Memristive Four-Wing Hyperchaotic System with Multiple Coexisting Attractors," Complexity, Hindawi, vol. 2020, pages 1-17, May.
    9. Volos, Ch. K. & Kyprianidis, I.M. & Stouboulos, I.N. & Vaidyanathan, S. & Pham, V.-T., 2016. "Analysis, adaptive control and circuit simulation of a novel nonlinear finance systemAuthor-Name: Tacha, O.I," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 200-217.
    10. Bocheng Bao & Aihuang Hu & Han Bao & Quan Xu & Mo Chen & Huagan Wu, 2018. "Three-Dimensional Memristive Hindmarsh–Rose Neuron Model with Hidden Coexisting Asymmetric Behaviors," Complexity, Hindawi, vol. 2018, pages 1-11, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ren, Lujie & Mou, Jun & Banerjee, Santo & Zhang, Yushu, 2023. "A hyperchaotic map with a new discrete memristor model: Design, dynamical analysis, implementation and application," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Jose-Cruz Nuñez-Perez & Vincent-Ademola Adeyemi & Yuma Sandoval-Ibarra & Francisco-Javier Perez-Pinal & Esteban Tlelo-Cuautle, 2021. "Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    3. Ma, Xujiong & Mou, Jun & Xiong, Li & Banerjee, Santo & Cao, Yinghong & Wang, Jieyang, 2021. "A novel chaotic circuit with coexistence of multiple attractors and state transition based on two memristors," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Wang, Jieyang & Mou, Jun & Xiong, Li & Zhang, Yingqian & Cao, Yinghong, 2021. "Fractional-order design of a novel non-autonomous laser chaotic system with compound nonlinearity and its circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Li, Xuejun & Mou, Jun & Banerjee, Santo & Wang, Zhisen & Cao, Yinghong, 2022. "Design and DSP implementation of a fractional-order detuned laser hyperchaotic circuit with applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    6. Huang, Pengfei & Chai, Yi & Chen, Xiaolong, 2022. "Multiple dynamics analysis of Lorenz-family systems and the application in signal detection," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    7. Gong, Li-Hua & Luo, Hui-Xin & Wu, Rou-Qing & Zhou, Nan-Run, 2022. "New 4D chaotic system with hidden attractors and self-excited attractors and its application in image encryption based on RNG," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    8. 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).
    9. Zain-Aldeen S. A. Rahman & Basil H. Jasim & Yasir I. A. Al-Yasir & Yim-Fun Hu & Raed A. Abd-Alhameed & Bilal Naji Alhasnawi, 2021. "A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications," Mathematics, MDPI, vol. 9(20), pages 1-25, October.
    10. Hemalatha Mahalingam & Thanikaiselvan Veeramalai & Anirudh Rajiv Menon & Subashanthini S. & Rengarajan Amirtharajan, 2023. "Dual-Domain Image Encryption in Unsecure Medium—A Secure Communication Perspective," Mathematics, MDPI, vol. 11(2), pages 1-23, January.
    11. Chen, Mo & Wang, Ankai & Wang, Chao & Wu, Huagan & Bao, Bocheng, 2022. "DC-offset-induced hidden and asymmetric dynamics in Memristive Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    12. Noel Freddy Fotie Foka & Balamurali Ramakrishnan & André Cheage Chamgoué & Alain Francis Talla & Victor Kamgang Kuetche, 2022. "Neuronal circuit based on Josephson junction actuated by a photocurrent: dynamical analysis and microcontroller implementation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(6), pages 1-8, June.
    13. Hu, Chenyang & Wang, Qiao & Zhang, Xiefu & Tian, Zean & Wu, Xianming, 2022. "A new chaotic system with novel multiple shapes of two-channel attractors," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bao, B. & Peol, M.A. & Bao, H. & Chen, M. & Li, H. & Chen, B., 2021. "No-argument memristive hyper-jerk system and its coexisting chaotic bubbles boosted by initial conditions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Chen, Mo & Ren, Xue & Wu, Huagan & Xu, Quan & Bao, Bocheng, 2020. "Interpreting initial offset boosting via reconstitution in integral domain," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Hu, Yongbing & Li, Qian & Ding, Dawei & Jiang, Li & Yang, Zongli & Zhang, Hongwei & Zhang, Zhixin, 2021. "Multiple coexisting analysis of a fractional-order coupled memristive system and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. 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).
    5. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    6. Peng, Yuexi & Sun, Kehui & He, Shaobo, 2020. "A discrete memristor model and its application in Hénon map," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. Du, Chuanhong & Liu, Licai & Zhang, Zhengping & Yu, Shixing, 2021. "Double memristors oscillator with hidden stacked attractors and its multi-transient and multistability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    8. Gu, Shuangquan & He, Shaobo & Wang, Huihai & Du, Baoxiang, 2021. "Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. Chen, Mo & Wang, Chao & Bao, Han & Ren, Xue & Bao, Bocheng & Xu, Quan, 2020. "Reconstitution for interpreting hidden dynamics with stable equilibrium point," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Bao, Han & Rong, Kang & Chen, Mo & Zhang, Xi & Bao, Bocheng, 2023. "Multistability and synchronization of discrete maps via memristive coupling," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    11. Vijayakumar, M.D. & Natiq, Hayder & Tametang Meli, Maxim Idriss & Leutcho, Gervais Dolvis & Tabekoueng Njitacke, Zeric, 2022. "Hamiltonian energy computation of a novel memristive mega-stable oscillator (MMO) with dissipative, conservative and repelled dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    12. Njitacke, Zeric Tabekoueng & Doubla, Isaac Sami & Mabekou, Sandrine & Kengne, Jacques, 2020. "Hidden electrical activity of two neurons connected with an asymmetric electric coupling subject to electromagnetic induction: Coexistence of patterns and its analog implementation," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    13. Du, Chuanhong & Liu, Licai & Zhang, Zhengping & Yu, Shixing, 2022. "A mem-element Wien-Bridge circuit with amplitude modulation and three kinds of offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    14. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    15. Lin, Y. & Liu, W.B. & Bao, H. & Shen, Q., 2020. "Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    16. Yu, Hui & Du, Shengzhi & Dong, Enzeng & Tong, Jigang, 2022. "Transient behaviors and equilibria-analysis-based boundary crisis analysis in a smooth 4D dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    17. Deng, Yue & Li, Yuxia, 2021. "Bifurcation and bursting oscillations in 2D non-autonomous discrete memristor-based hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    18. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    19. Takhi, Hocine & Kemih, Karim & Moysis, Lazaros & Volos, Christos, 2021. "Passivity based sliding mode control and synchronization of a perturbed uncertain unified chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 150-169.
    20. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001430. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.