Bifurcation analysis of delay-induced resonances of the El-Nino Southern Oscillation

Details Bifurcation analysis of delay-induced resonances of the El-Nino Southern Oscillation Bifurcation analysis of delay-induced resonances of the El-Nino Southern Oscillation

2011-09-13

arxiv.org/abs/1109.2818v1

Mathematics

Dynamical Systems

19 pages, 7 figures, initial submitted version

Scientific paper

Models of global climate phenomena of low to intermediate complexity are very useful for providing an understanding at a conceptual level. An important aspect of such models is the presence of a number of feedback loops that feature considerable delay times, usually due to the time it takes to transport energy (for example, in the form of hot/cold air or water) around the globe. In this paper we demonstrate how one can performed a bifurcation analysis of the behaviour of a periodically forced delay differential equation (DDE) in dependence on key parameters. As a concrete example we consider the El-Nino Southern Oscillation (ENSO), which is a sea surface temperature oscillation on a multi-year scale in the basin of the Pacific Ocean. One can think of ENSO as being generated by an interplay between two feedback effects, one positive and one negative, which act only after some delay that is determined by the speed of transport of sea-surface temperature anomalies across the Pacific. We perform here a case study of a simple delay-induced oscillator model for ENSO (introduced by Tziperman et al, J. Climate 11 (1998)), which incorporates the two feedback effects and is parametrically forced by annual variation. More specifically, we use numerical bifurcation analysis tools to explore directly regions of delay-induced resonances and other stability boundaries in this DDE model for ENSO.

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