The effect of state dependence in a delay differential equation model for the El Niño Southern Oscillation
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Accepted Version
Date
2019-07-22
Authors
Keane, Andrew
Krauskopf, Bernd
Dijkstra, Henk A.
Journal Title
Journal ISSN
Volume Title
Publisher
The Royal Society
Published Version
Abstract
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.
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Keywords
Climate modelling , ENSO , Delay differential equations , Bifurcation analysis , Non-constant delays
Citation
Keane, A., Krauskopf, B.and Dijkstra H. A. (2019) 'The effect of state dependence in a delay differential equation model for the El Niño Southern Oscillation', Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377, 20180121 (23pp). https://doi.org/10.1098/rsta.2018.0121