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The Madden-Julian Oscillation (MJO) and the El Ni\~no-Southern Oscillation (ENSO) are two dominant modes of tropical climate variability, each with profound global weather impacts. While their individual dynamics have been widely studied,…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
The Ghil-Zaliapin-Thompson (GZT) model, a scalar delay differential equation with periodic forcing and time-delayed feedback, captures key features of the El Nino-Southern Oscillation (ENSO) phenomenon. Numerical studies of the GZT model…
Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…
The El Ni{~n}o-Southern Oscillation (ENSO) exerts profound influence on global climate variability, yet its prediction remains a grand challenge. Recent advances in deep learning have significantly improved forecasting skill, but the…
The impact of the El Ni\~no-Southern Oscillation (ENSO) on the extratropics is investigated in an idealized, reduced-order model that has a tropical and an extratropical module. Unidirectional ENSO forcing is used to mimick the atmospheric…
Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological systems, this instability may…
Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig…
We study the three-timescale dynamics of a model that describes the El Ni\~no Southern Oscillation (ENSO) phenomenon, which was proposed in [A. Roberts, J. Guckenheimer, E. Widiasih, A. Timmermann, and C. K. Jones, Mixed-mode oscillations…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
Understanding the interactions between the El Nino-Southern Oscillation (ENSO) and the Madden-Julian Oscillation (MJO) is essential to studying climate variabilities and predicting extreme weather events. Here, we develop a stochastic…
The purpose of this review-and-research paper is twofold: (i) to review the role played in climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and reduction of the uncertainties in future climate-change…
Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems. For instance, increased greenhouse gas concentrations are predicted to lead to drastic decreases in low…
We introduce an interpretable-by-design method, optimized model-analog, that integrates deep learning with model-analog forecasting which generates forecasts from similar initial climate states in a repository of model simulations. This…
El Ni\~no Southern Oscillation (ENSO) is the Earth's strongest source of interannual climate variability. Although its center of action is in the tropical Pacific, it has significant influences on the climate at the planetary scale. ENSO is…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
El Ni\~no Southern Oscillation (ENSO) diversity is characterized based on the longitudinal location of maximum sea surface temperature anomalies (SSTA) and amplitude in the tropical Pacific, as Central Pacific (CP) events are typically…
We revisit the classical Suarez-Schopf delayed oscillator. Special attention is paid to the region of linear stability in the space of parameters. By means of the theory of inertial manifolds developed in our adjacent papers, we provide…
We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with…
Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing…