Keane Andrew, Krauskopf Bernd, Dijkstra Henk A
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand.
Department of Physics, Center for Complex Systems Studies, Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, The Netherlands.
Philos Trans A Math Phys Eng Sci. 2019 Sep 9;377(2153):20180121. doi: 10.1098/rsta.2018.0121. Epub 2019 Jul 22.
Delay differential equations (DDEs) have been used successfully in the past to model climate systems at a conceptual level. An important aspect of these models is the existence of feedback loops that feature a delay time, usually associated with the time required to transport energy through the atmosphere and/or oceans across the globe. So far, such delays are generally assumed to be constant. Recent studies have demonstrated that even simple DDEs with non-constant delay times, which change depending on the state of the system, can produce surprisingly rich dynamical behaviour. Here, we present arguments for the state dependence of the delay in a DDE model for the El Niño Southern Oscillation phenomenon in the climate system. We then conduct a bifurcation analysis by means of continuation software to investigate the effect of state dependence in the delay on the observed dynamics of the system. More specifically, we show that the underlying delay-induced structure of resonance regions may change considerably in the presence of state dependence. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.
延迟微分方程（DDEs）过去已成功用于在概念层面上对气候系统进行建模。这些模型的一个重要方面是存在具有延迟时间的反馈回路，该延迟时间通常与能量在全球范围内通过大气和/或海洋传输所需的时间相关。到目前为止，此类延迟通常被假定为恒定的。最近的研究表明，即使是具有非恒定延迟时间（其根据系统状态而变化）的简单DDEs，也能产生令人惊讶的丰富动力学行为。在此，我们提出关于气候系统中厄尔尼诺 - 南方涛动现象的DDE模型中延迟的状态依赖性的论据。然后，我们通过延拓软件进行分岔分析，以研究延迟中的状态依赖性对系统观测动力学的影响。更具体地说，我们表明在存在状态依赖性的情况下，共振区域潜在的延迟诱导结构可能会发生相当大的变化。本文是主题为“延迟系统的非线性动力学”的一部分。
