IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v185y2024ics0960077924005708.html
   My bibliography  Save this article

Global dynamics of a hexagonal governor system with two time delays in the parameter and state spaces

Author

Listed:
  • Deng, Shuning
  • Ji, Jinchen
  • Wen, Guilin
  • Yin, Shan

Abstract

This paper investigates the global dynamics of a hexagonal governor system under two varying time delays, where one time delay originates from the working principle of the engine and the operation of an equivalent mass-spring structure causes the other. Firstly, based on the established time-delayed governor model, the combined impact of these time delays on the stability of equilibrium is investigated, and the local bifurcation behaviors of equilibrium are analyzed via the method of multiple scales. Subsequently, the global correlation between system responses and parameter combinations is explored using a two-parameter co-simulation scheme, which incorporates a dimension reduction technique for the time-delayed system, the largest Lyapunov exponent, and the parallel computing technique. Furthermore, the bifurcation laws of various system responses and potential chaotic routes are studied through one-parameter bifurcation analyses. Considering the intricate operational environment and uncertain external disturbances, the steady-state response of the delayed governor system is further studied under a large number of initial conditions. To achieve this goal, a numerical strategy is proposed that incorporates a dimension reduction technique for the time-delayed system, the method of cell mapping, and the probability of convergence. Using this numerical strategy, the multi-stability behavior of the time-delayed governor system is thoroughly investigated, and the effectiveness of this numerical method is validated through the one-parameter bifurcation analysis. The revealed dynamic behavior would provide a deeper understanding of the time-delayed governor dynamics in both the parameter and state spaces. It is mentioned that the presented numerical strategies are also applicable in the design and motion control of other nonlinear dynamical systems with time delay effects, such as the time-delayed vibration absorbers and isolators.

Suggested Citation

  • Deng, Shuning & Ji, Jinchen & Wen, Guilin & Yin, Shan, 2024. "Global dynamics of a hexagonal governor system with two time delays in the parameter and state spaces," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924005708
    DOI: 10.1016/j.chaos.2024.115018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924005708
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115018?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. Zhang, Jian-Gang & Li, Xian-Feng & Chu, Yan-Dong & Yu, Jian-Ning & Chang, Ying-Xiang, 2009. "Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2150-2168.
    2. Stefanski, Andrzej & Dabrowski, Artur & Kapitaniak, Tomasz, 2005. "Evaluation of the largest Lyapunov exponent in dynamical systems with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1651-1659.
    3. Deng, Shuning & Ji, Jinchen & Wen, Guilin & Xu, Huidong, 2021. "A comparative study of the dynamics of a three-disk dynamo system with and without time delay," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    4. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    5. Xu, Beibei & Chen, Diyi & Zhang, Hao & Wang, Feifei, 2015. "Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 50-61.
    6. Zhang, Cun-Hua & He, Ye, 2020. "Multiple stability switches and Hopf bifurcations induced by the delay in a Lengyel-Epstein chemical reaction system," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    7. Ge, Zheng-Ming & Lee, Ching-I, 2005. "Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1855-1864.
    8. Alidousti, J. & Eskandari, Z., 2021. "Dynamical behavior and Poincare section of fractional-order centrifugal governor system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 791-806.
    9. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.
    10. Li Zhang & Xinlei An & Jiangang Zhang & Qianqian Shi & M. De Aguiar, 2022. "Bifurcation Analysis and Synchronous Patterns between Field Coupled Neurons with Time Delay," Complexity, Hindawi, vol. 2022, pages 1-19, June.
    11. David S. Glass & Xiaofan Jin & Ingmar H. Riedel-Kruse, 2021. "Nonlinear delay differential equations and their application to modeling biological network motifs," Nature Communications, Nature, vol. 12(1), pages 1-19, December.
    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. Yan, Jun-Juh & Lin, Jui-Sheng & Liao, Teh-Lu, 2007. "Robust dynamic compensator for a class of time delay systems containing saturating control input," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1223-1231.
    2. Yang, Yanling & Wang, Qiubao, 2023. "Capture of stochastic P-bifurcation in a delayed mechanical centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Margielewicz, Jerzy & Gąska, Damian & Litak, Grzegorz & Wolszczak, Piotr & Yurchenko, Daniil, 2022. "Nonlinear dynamics of a new energy harvesting system with quasi-zero stiffness," Applied Energy, Elsevier, vol. 307(C).
    4. Margielewicz, Jerzy & Gąska, Damian & Litak, Grzegorz, 2019. "Evolution of the geometric structure of strange attractors of a quasi-zero stiffness vibration isolator," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 47-57.
    5. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    6. Tan, Zengqiang & Zhang, Chengjian, 2022. "Numerical approximation to semi-linear stiff neutral equations via implicit–explicit general linear methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 68-87.
    7. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    8. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    9. Zhou, Biliu & Jin, Yanfei & Xu, Huidong, 2022. "Global dynamics for a class of tristable system with negative stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    11. Amat, Sergio & José Legaz, M. & Pedregal, Pablo, 2015. "A variable step-size implementation of a variational method for stiff differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 49-57.
    12. García, M.A. & Castro, M.A. & Martín, J.A. & Rodríguez, F., 2018. "Exact and nonstandard numerical schemes for linear delay differential models," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 337-345.
    13. Zhan, Rui & Fang, Jinwei, 2024. "Stability analysis of explicit exponential Rosenbrock methods for stiff differential equations with constant delay," Applied Mathematics and Computation, Elsevier, vol. 482(C).
    14. Xu, Changjin & Liu, Zixin & Liao, Maoxin & Li, Peiluan & Xiao, Qimei & Yuan, Shuai, 2021. "Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 471-494.
    15. M. Motawi Khashan & Rohul Amin & Muhammed I. Syam, 2019. "A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    16. Liu, Yi & Zhang, Jian & Liu, Zhe & Chen, Long & Yu, Xiaodong, 2022. "Surge wave characteristics for hydropower plant with upstream double surge tanks connected in series under small load disturbance," Renewable Energy, Elsevier, vol. 186(C), pages 667-676.
    17. O. A. Rosas-Jaimes & G. A. Munoz-Hernandez & G. Mino-Aguilar & J. Castaneda-Camacho & C. A. Gracios-Marin, 2019. "Evaluating Fractional PID Control in a Nonlinear MIMO Model of a Hydroelectric Power Station," Complexity, Hindawi, vol. 2019, pages 1-15, January.
    18. Chen, Jinbao & Zheng, Yang & Liu, Dong & Du, Yang & Xiao, Zhihuai, 2023. "Quantitative stability analysis of complex nonlinear hydraulic turbine regulation system based on accurate calculation," Applied Energy, Elsevier, vol. 351(C).
    19. Olaf Posch & Timo Trimborn, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Economics Working Papers 2010-08, Department of Economics and Business Economics, Aarhus University.
    20. Tan, Zengqiang & Zhang, Chengjian, 2018. "Implicit-explicit one-leg methods for nonlinear stiff neutral equations," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 196-210.

    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:185:y:2024:i:c:s0960077924005708. 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.