This paper aims to report a new route to pulse-shaped explosion (PSE) related to the limit cycle attractor in a mechanical system with multiple-frequency excitations. We show that the compound bursting connected by PSE of equilibria can be observed in this system. Then, with the decrease of the amplitude of parametric excitation, the compound bursting pattern begins to change to other types, accompanied by the generation of PSE of limit cycles. Typically, as a novel sharp transition behavior underlying the occurrence of bursting oscillations, the PSE can be created by the disappearance of critical escape transitions. In present study, based on the two-parameter bifurcation analysis, we find that the PSE can also be created in the branch of limit cycles with the disappearance of fold points of homoclinic bifurcation curves, which is quite different from the ones reported in previous works and can be regarded as a new route to the PSE of limit cycles. Based on this, the compound bursting induced by the PSE of limit cycles is investigated. Besides, it should be pointed out that the limit cycle exhibiting PSE can be regarded as an amplitude-modulated limit cycle attractor, and thus we obtain a newly released bursting rhythm, namely the amplitude-modulated bursting, based on the PSE of limit cycles. These findings have significant implications for the understanding of PSE and the diversity of bursting dynamics induced by it.

本文旨在报告与具有多频激励的机械系统中的极限环吸引子相关的脉冲形爆炸 (PSE) 的新途径。我们表明，在该系统中可以观察到由平衡的 PSE 连接的化合物爆发。然后，随着参量激发幅值的减小，复合爆发模式开始向其他类型转变，同时伴随着极限环PSE的产生。通常，作为突发振荡发生背后的一种新的急剧过渡行为，PSE 可以通过关键逃逸过渡的消失来创建。在本研究中，基于二参数分岔分析，我们发现随着同宿分岔曲线折叠点的消失，PSE也可以在极限环的分支中产生，这与以前的工作中报道的有很大不同，可以看作是极限环PSE的新途径。在此基础上，研究了极限环PSE引起的复合爆裂。此外，需要指出的是，表现出PSE的极限环可以看作是一个调幅极限环吸引子，因此我们基于极限环的PSE得到了一个新发布的爆发节奏，即调幅爆发。这些发现对理解 PSE 及其引起的爆发动力学的多样性具有重要意义。需要指出的是，表现出PSE的极限环可以看作是一个调幅的极限环吸引子，因此我们基于极限环的PSE得到了一个新发布的爆发节奏，即调幅爆发。这些发现对理解 PSE 及其引起的爆发动力学的多样性具有重要意义。需要指出的是，表现出PSE的极限环可以看作是一个调幅的极限环吸引子，因此我们基于极限环的PSE得到了一个新发布的爆发节奏，即调幅爆发。这些发现对理解 PSE 及其引起的爆发动力学的多样性具有重要意义。