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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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