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Abstract The Earth’s climate system is a classical example of a multiscale, multiphysics dynamical system with an extremely large number of active degrees of freedom, exhibiting variability on scales ranging from micrometers and seconds in cloud microphysics, to thousands of kilometers and centuries in ocean dynamics. Yet, despite this dynamical complexity, climate dynamics is known to exhibit coherent modes of variability. A primary example is the El Niño Southern Oscillation (ENSO), the dominant mode of interannual (3–5 yr) variability in the climate system. The objective and robust characterization of this and other important phenomena presents a long-standing challenge in Earth system science, the resolution of which would lead to improved scientific understanding and prediction of climate dynamics, as well as assessment of their impacts on human and natural systems. Here, we show that the spectral theory of dynamical systems, combined with techniques from data science, provides an effective means for extracting coherent modes of climate variability from high-dimensional model and observational data, requiring no frequency prefiltering, but recovering multiple timescales and their interactions. Lifecycle composites of ENSO are shown to improve upon results from conventional indices in terms of dynamical consistency and physical interpretability. In addition, the role of combination modes between ENSO and the annual cycle in ENSO diversity is elucidated. 

In this article, we devise two related control algorithms to change the degree of synchrony of a population of noise-free, identical, uncoupled neural oscillators using a single control input. The algorithms are based on phase reduction, and use a population-level partial differential equation formulation to change the phase distribution of the neurons as desired. Motivated by the pathological neural synchronization hypothesized to be present in patients suffering from essential and parkinsonian tremor, we take our control objective to be the desynchronization of an initially synchronized neural population. Through numerical simulations, we are able to show that our algorithms work for both Type I and Type II neural populations. To demonstrate the versatility of our control algorithms, we also show that they can be applied to synchronize an initially desynchronized neural population as well. For the systems considered in this paper, the control algorithms can be applied to achieve any desired traveling-wave neural phase distribution, as long as the combination of initial and desired phase distributions is non-degenerate.