Abstract The dynamic behavior of a fractional governor system is studied in this paper. The Stability and bifurcation of the equilibrium points of the system are investigated. We derive specific conditions for which the Hopf bifurcation of the fractional governor system may occur. It can be seen that different results are obtained compared to the classical mode. In the non-autonomous system, the tendency towards chaos is investigated using diagrams of bifurcation and Poincare maps analysis. Finally, the numerical results are given to illustrate the theoretical results. Analytical and numerical simulations result could be extended to other systems and ultimately, these results could be applied as a technical tool for the control and rotary machine designers.

中文翻译：

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分数阶离心调速器系统的动力学行为和庞加莱截面

摘要 本文研究了分数阶调速器系统的动态行为。研究了系统平衡点的稳定性和分岔。我们推导出分式调节器系统可能发生 Hopf 分叉的特定条件。可以看出，与经典模式相比，得到了不同的结果。在非自治系统中，使用分叉图和庞加莱图分析来研究混沌趋势。最后，给出数值结果来说明理论结果。分析和数值模拟结果可以扩展到其他系统，最终，这些结果可以用作控制和旋转机械设计人员的技术工具。