Complex oscillatory dynamics in a three-timescale El Ni & ntilde;o Southern Oscillation model

We study the three-timescale dynamics of a model that describes the El Nino Southern Oscillation (ENSO) phenomenon, which was proposed in Roberts et al. (2016). While ENSO phenomena are in-herently 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 model exhibits a variety of qualitatively different behaviours in that regime, 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 for this particular model. 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.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).