快慢尺度下的奇异向量场具有复杂的动力学行为，揭示其复杂簇发现象的产生机制对于电子电路和大型机械转子系统等工程领域具有一定的应用价值。本项目拟研究Fold条件下奇异向量场的簇发行为及其诱发机制。首先，计算实际系统在Fold条件下规范型向量场的显式表达，考察参数变化对奇异向量场动力学特性的影响，建立参数与向量场动力学特性之间的对应关系；其次，分析不同形式周期激励作用下奇异向量场在不同分岔模式之间的转换行为，重点研究其在快慢转迁时的高余维分岔机理，探讨系统通往复杂振荡的演化过程以及复杂运动的特点；最后，构建LCR振荡电路，研究实验电路的准确性和有效性的同时验证理论分析的结果和数值模拟的动力学现象。本项目对于深入理解各种新簇发现象的本质具有科学意义，为避免在实际应用中发生此类现象提供理论依据和技术支撑。

The singular vector field on the fast-slow scale has complex dynamic behaviors. Revealing the mechanism of the complex bursting phenomenons has certain application value in engineering fields such as electronic circuits and large mechanical rotor systems. This project intends to focus on studying the bursting oscillations behaviors and the inducing mechanism of fast-slow singular vector field under compound fold conditons. Firstly, we will calculate the explicit expression of vector field of the engineering system under fold condition, and investigate the dynamic characteristics of the singular vector field via multi-parameter changes. In particular, this project will establish the corresponding relationship between the parameters and the dynamic characteristics of the vector field. Afterward, through different forms of periodic excitation, we will analyze the transformation behaviors of singular vector field between various modes of bifurcation. This project focus on studying the mechanism of high codimensional bifurcation in fast and slow transition, and investigating the evolution of the system to complex oscillation and the characteristics of complex motion. Finally, the results of theoretical analysis and numerical simulation will be verified via taking the LCR oscillation circuit as the experimental object. This project is of scientific significance for the in-depth understanding the essence of various new bursting phenomenas and provides theoretical basis and technical support for the avoidance of such phenomenas in practical engineering applications.