We reproduce nonlinear behaviors, including frequency chirping and mode splitting, referred to as bump-on-tail instabilities. As has been reported in previous works, the generation and motion of phase-space hole-clump pairs in a kinetically driven, dissipative system can result in frequency chirping. We provide examples of frequency chirping, both with and without pure diffusion, in order to illustrate the role of the diffusion effect, which can suppress holes and clumps; Asymmetric frequency chirpings are produced with drag effect, which is essential to enhance holes, and suppress clumps. Although both diffusion and drag effect suppress the clumps, downward sweepings are observed, caused by a complicated interaction of diffusion and drag. In addition, we examine the discrepancies in frequency chirping between marginally unstable, and far from marginally unstable cases, which we elucidate by means of a dissipative system. In addition, mode splitting is also produced via BOT code for a marginal case with large diffusion.

我们重现非线性行为，包括频率啁啾和模式分裂，称为尾部颠簸不稳定性。正如之前的工作所报道的，在动力学驱动的耗散系统中，相空间空穴对的产生和运动会导致频率啁啾。我们提供了频率啁啾的例子，包括纯扩散和不扩散，以说明扩散效应的作用，它可以抑制空穴和团块；非对称频率啁啾产生具有阻力效应，这对于增强孔洞和抑制团块至关重要。虽然扩散和阻力效应都抑制了团块，但观察到向下扫掠，这是由扩散和阻力的复杂相互作用引起的。此外，我们检查了边缘不稳定之间的频率啁啾差异，与我们通过耗散系统阐明的边缘不稳定的情况相去甚远。此外，对于具有大扩散的边缘情况，也可以通过 BOT 代码产生模式分裂。