The main objects of this paper focus on the complex dynamics and chaos control of an electromagnetic valve train (EMV). A variety of periodic solutions and nonlinear phenomena can be expressed using various numerical techniques such as time responses, phase portraits, Poincaré maps, and frequency spectra. The effects of varying the system parameters can be observed in the bifurcation diagram. It shows that this system can undergo a cascade of period-doubling bifurcations prior to the onset of chaos. Lyapunov exponents and Lyapunov dimensions are employed to confirm chaotic behavior for EMV. A proposed continuous feedback control method based on synchronization characteristics eliminated chaotic oscillations. Numerical simulations are utilized to verify the feasibility and efficiency of the proposed control technique. Finally, some robustness analysis of parametric perturbation on EMV system with synchronization control is confirmed by Lyapunov stability theory and numerical simulations.

中文翻译：

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无凸轮发动机电磁气门机构的分岔、混沌路径和同步混沌

本文的主要对象集中在电磁阀机构 (EMV) 的复杂动力学和混沌控制上。可以使用各种数值技术（例如时间响应、相图、庞加莱图和频谱）来表示各种周期解和非线性现象。可以在分叉图中观察到改变系统参数的影响。它表明该系统可以在混沌开始之前经历一连串倍周期分岔。Lyapunov 指数和 Lyapunov 维数用于确认 EMV 的混沌行为。提出的基于同步特性的连续反馈控制方法消除了混沌振荡。数值模拟被用来验证所提出的控制技术的可行性和效率。最后，