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

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  • 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
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    References listed on IDEAS

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    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, Decembrie.
    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.
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