IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i2p198-d1563528.html
   My bibliography  Save this article

Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0

Author

Listed:
  • Ming Chen

    (School of General Education, Hubei College of Chinese Medicine, Jingzhou 434020, China)

  • Xueshuai Zhu

    (School of Chemical and Environmental Engineering, China University of Mining and Technology, Beijing 100083, China)

Abstract

The switched arrival system is a typical hybrid system that is commonly used to simulate industrial control systems. The corresponding mathematical model and switching time are described. In order to be closer to the actual industrial control systems, the switching time is changed from 0 to greater than 0. In this case, the system not only generates chaos but also system losses. For this purpose, firstly, the causes of system losses are analyzed. Secondly, the Poincare section is selected to define the control target—periodic orbits. And then, the delayed impulsive feedback method is improved for the system at a switching time greater than 0, and extended to each boundary in order to enhance the control effect. This not only controls chaos in the system but also reduces the loss ratio and detects periodic orbits. Finally, numerical simulations of the system orbits and loss ratio with and without implementing control are compared. The possible intervals for the optimal control coefficient under the same initial conditions are detected. Period-1 orbits are detected at switching times greater than 0, and the stability of system operation is verified.

Suggested Citation

  • Ming Chen & Xueshuai Zhu, 2025. "Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0," Mathematics, MDPI, vol. 13(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:198-:d:1563528
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/2/198/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/2/198/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    2. Fucheng Liao & Lijie Cui & Yanrong Lu & Jiamei Deng, 2020. "Preview Tracking Control of Linear Periodic Switched Systems with Dwell Time," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, October.
    3. Ruofeng Rao & Quanxin Zhu, 2024. "Synchronization for Reaction–Diffusion Switched Delayed Feedback Epidemic Systems via Impulsive Control," Mathematics, MDPI, vol. 12(3), pages 1-12, January.
    4. Chun Zhang & Qiaoxia Tang & Zhixiang Wang, 2022. "Grazing and Symmetry-Breaking Bifurcations Induced Oscillations in a Switched System Composed of Duffing and van der Pol Oscillators," Mathematics, MDPI, vol. 10(5), pages 1-10, February.
    Full references (including those not matched with items on IDEAS)

    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. Sergey Kashchenko, 2023. "Van der Pol Equation with a Large Feedback Delay," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    2. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    3. Rhaima, Mohamed, 2023. "Ulam–Hyers stability for an impulsive Caputo–Hadamard fractional neutral stochastic differential equations with infinite delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 281-295.
    4. Natalya O. Sedova & Olga V. Druzhinina, 2023. "Exponential Stability of Nonlinear Time-Varying Delay Differential Equations via Lyapunov–Razumikhin Technique," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    5. Chunsheng Wang & Xiangdong Liu & Feng Jiao & Hong Mai & Han Chen & Runpeng Lin, 2023. "Generalized Halanay Inequalities and Relative Application to Time-Delay Dynamical Systems," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
    6. Li, Jing & Zhu, Quanxin, 2023. "Event-triggered impulsive control of stochastic functional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Quanxin Zhu, 2022. "Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering," Mathematics, MDPI, vol. 10(24), pages 1-2, December.
    8. Yong Tang, 2023. "Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model," Mathematics, MDPI, vol. 11(11), pages 1-12, June.
    9. Haiqing Du & Xiaojing Wang & Bo Du, 2023. "Positive Periodic Solution for Pipe/Tank Flow Configurations with Friction," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
    10. Zhengqi Ma & Shoucheng Yuan & Kexin Meng & Shuli Mei, 2023. "Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    11. Qing Yang & Xiaojing Wang & Xiwang Cheng & Bo Du & Yuxiao Zhao, 2023. "Positive Periodic Solution for Neutral-Type Integral Differential Equation Arising in Epidemic Model," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    12. Liu, Zhiguang & Zhu, Quanxin, 2023. "Ultimate boundedness of impulsive stochastic delay differential equations with delayed impulses," Statistics & Probability Letters, Elsevier, vol. 199(C).
    13. Chun Zhang & Qiaoxia Tang & Zhixiang Wang, 2022. "Grazing and Symmetry-Breaking Bifurcations Induced Oscillations in a Switched System Composed of Duffing and van der Pol Oscillators," Mathematics, MDPI, vol. 10(5), pages 1-10, February.
    14. Yazid Alhojilan & Hamdy M. Ahmed, 2023. "New Results Concerning Approximate Controllability of Conformable Fractional Noninstantaneous Impulsive Stochastic Evolution Equations via Poisson Jumps," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    15. Bahua Lin & Zhan Zhou, 2023. "Positive Solutions to the Discrete Boundary Value Problem of the Kirchhoff Type," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    16. Yuxiao Zhao & Linshan Wang, 2022. "Practical Exponential Stability of Impulsive Stochastic Food Chain System with Time-Varying Delays," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    17. Hongguang Fan & Jiahui Tang & Kaibo Shi & Yi Zhao & Hui Wen, 2023. "Delayed Impulsive Control for μ -Synchronization of Nonlinear Multi-Weighted Complex Networks with Uncertain Parameter Perturbation and Unbounded Delays," Mathematics, MDPI, vol. 11(1), pages 1-17, January.
    18. Zhao Li & Chen Peng, 2023. "Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    19. Mahtab Mehrabbeik & Atefeh Ahmadi & Fatemeh Bakouie & Amir Homayoun Jafari & Sajad Jafari & Dibakar Ghosh, 2023. "The Impact of Higher-Order Interactions on the Synchronization of Hindmarsh–Rose Neuron Maps under Different Coupling Functions," Mathematics, MDPI, vol. 11(13), pages 1-18, June.
    20. Wael W. Mohammed & Clemente Cesarano & Farah M. Al-Askar & Mahmoud El-Morshedy, 2022. "Solitary Wave Solutions for the Stochastic Fractional-Space KdV in the Sense of the M-Truncated Derivative," Mathematics, MDPI, vol. 10(24), pages 1-11, December.

    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:gam:jmathe:v:13:y:2025:i:2:p:198-:d:1563528. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.