论文标题
在三段时间的厄尔尼诺南部振荡模型中复杂的振荡动力学
Complex oscillatory dynamics in a three-timescale El Niño Southern Oscillation model
论文作者
论文摘要
我们研究了一个描述厄尔尼诺南部振荡（ENSO）现象的模型的三频动力学，该模型是在[A. Roberts，J。Guckenheimer，E。Widiasih，A。Timmermann和C. K. Jones，ElNiño-Southern振荡的混合模式振荡，《大气科学杂志》，第73页（2016年），第1755555555----1766页。尽管ENSO现象本质上以多个不同的时间表的存在为特征，但以前仅在两个时间尺度的环境中研究了上述模型。 Here, we uncover the geometric mechanisms that are responsible for complex oscillatory dynamics in a three-timescale regime, and we demonstrate that the system exhibits a variety of qualitatively different behaviours, such as mixed-mode oscillation (MMO) with ``plateaus" -- trajectories where epochs of quiescence alternate with dramatic excursions -- and relaxation oscillation. The latter, although emergent also in the此外，以前没有记录过两个时间的上下文，我们证明这些机制与其他生态和人口动态的模型有关，因为基础几何形状与Rosenzweig--Macarthur型模型的展开相似。
We study the three-timescale dynamics of a model that describes the El Niño Southern Oscillation (ENSO) phenomenon, which was proposed in [A. Roberts, J. Guckenheimer, E. Widiasih, A. Timmermann, and C. K. Jones, Mixed-mode oscillations of El Niño--Southern Oscillation, Journal of the Atmospheric Sciences, 73 (2016), pp. 1755--1766]. While ENSO phenomena are inherently characterised by the presence of multiple distinct timescales, the above model has previously been studied in a two-timescale context only. Here, we uncover the geometric mechanisms that are responsible for complex oscillatory dynamics in a three-timescale regime, and we demonstrate that the system exhibits a variety of qualitatively different behaviours, such as mixed-mode oscillation (MMO) with ``plateaus" -- trajectories where epochs of quiescence alternate with dramatic excursions -- and relaxation oscillation. The latter, although emergent also in the two-timescale context in appropriate parameter regimes, had not been documented previously. Moreover, we show that these mechanisms are relevant to models from other fields of ecological and population dynamics, as the underlying geometry is similar to the unfolding of Rosenzweig--MacArthur-type models in three dimensions.
