具有最小延迟的厄尔尼诺-南方涛动分布式延迟模型：移位线性链技巧的案例研究
A distributed-delay model for the El Niño Southern Oscillation with a minimum delay: a case study of the shifted linear chain trick
- The University of Auckland（奥克兰大学）
- University College Cork（科克大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出移位厄兰核与线性链技巧，对具有最小延迟的厄尔尼诺-南方涛动分布式延迟模型进行分岔分析，揭示不同分布宽度下的共振结构。
AI中文摘要：
在使用延迟微分方程对感兴趣的系统进行建模时，当延迟响应发生在显著的时间范围内而非单一恒定延迟时，分布式延迟可能是合适的建模选择。然而，在具有最小物理传输或处理时间的系统中，延迟核应尊重一个固定且正的最小延迟。移位厄兰核是一个方便的选择，因为移位线性链技巧允许将与此类核相关的卷积替换为具有一个恒定延迟的有限辅助变量表示。正如我们通过对具有季节性强迫和分布式延迟海洋反馈的 Ghil-Zaliapin-Thompson (GZT) 厄尔尼诺-南方涛动模型的案例研究所展示的，这种简化使得对于任何宽度的厄兰分布，都可以使用数值延拓技术进行分岔分析。具体而言，我们针对不同分布宽度，在强迫强度和延迟平面上展示了分布式延迟 GZT 模型的分岔和共振结构。为确保同类比较并确定延迟分布的影响，我们以有效延迟的形式呈现这些结果，此外，还重新缩放反馈强度以考虑其随分布宽度增加而衰减的影响。
英文摘要：
When modelling a system of interest with a delay differential equation, a distributed delay may be the appropriate modelling choice when the delayed response occurs over a significant range of times rather than with a single constant delay. In systems with a minimum physical transit or processing time, however, the delay kernel should respect a fixed and positive minimum delay. A shifted Erlang kernel is a convenient choice, because the shifted linear chain trick allows one to replace the convolution associated with this type of kernel by a finite auxiliary-variable representation with one constant delay. As we demonstrate with a case study of the Ghil-Zaliapin-Thompson (GZT) model of the El Niño Southern Oscillation with seasonal forcing and distributed delayed oceanic feedback, this reduction makes it possible to perform a bifurcation analysis with numerical continuation techniques for any width of the Erlang distribution. Specifically, we present the bifurcation and resonance structure of the distributed-delay GZT model in the plane of forcing strength and delay for different widths of the distribution. To ensure a like-for-like comparison and determine the influence of delay distribution, we present these results in terms of the effective delay and, moreover, rescale the feedback strength to account for its attenuation with increasing width of the distribution.
