Review article: Dynamical systems, algebraic topology and the climate sciences by M. Ghil, M. Ghil, M. Ghil, D. Sciamarella, D. Sciamarella, D. Sciamarella

“…<p>The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of this theory have percolated into the climate sciences as early as the 1960s. …”
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Hilbert problems for the geosciences in the 21st century by M. Ghil

“…The framework is that of dynamical systems theory, with an emphasis on successive bifurcations and the ergodic theory of nonlinear systems. …”
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Human Brain Networks: Spiking Neuron Models, Multistability, Synchronization, Thermodynamics, Maximum Entropy Production, and Anesthetic Cascade Mechanisms by Wassim M. Haddad, Qing Hui, James M. Bailey

“…A key application of nonlinear dynamical systems theory to the neurosciences is to study phenomena of the central nervous system that exhibit nearly discontinuous transitions between macroscopic states. …”
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The Continuum Between Temperament and Mental Illness as Dynamical Phases and Transitions by William Sulis

“…The application of complex adaptive dynamical systems theory has led to a host of markers including geometrical markers (periodicity, intermittency, recurrence, chaos) and analytical markers such as fluctuation spectroscopy, scaling, entropy, recurrence time. …”
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Mutual beta power modulation in dyadic entrainment by Mattia Rosso, Ole A. Heggli, Pieter J. Maes, Peter Vuust, Marc Leman

“…Traditionally, this phenomenon has been explained from the perspectives of predictive coding or dynamical systems theory. While these theories diverge with respect to whether individuals hold internal models of each other, they both assume a predictive or anticipatory mechanism enabling rhythmic interactions. …”
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On a Dynamical Approach to Some Prime Number Sequences by Lucas Lacasa, Bartolome Luque, Ignacio Gómez, Octavio Miramontes

“…We show how the cross-disciplinary transfer of techniques from dynamical systems theory to number theory can be a fruitful avenue for research. …”
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Re-Thinking the World with Neutral Monism:Removing the Boundaries Between Mind, Matter, and Spacetime by Michael Silberstein, William Stuckey

“…Herein we are not interested in merely using dynamical systems theory, graph theory, information theory, etc., to model the relationship between brain dynamics and networks, and various states and degrees of conscious processes. …”
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Impact of different destocking strategies on the resilience of dry rangelands by Toyo Vignal, Mara Baudena, Angeles Garcia Mayor, Jonathan A. Sherratt

“…We study analytically the impact of varying the stocking density and the destocking adaptivity on the resilience of the system to the effects of drought. By using dynamical systems theory, we look at how different measures of resilience are affected by variations in destocking strategies. …”
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Weather types across the Maritime Continent: From the diurnal cycle to interannual variations by Vincent eMoron, Vincent eMoron, Andrew William Robertson, Jian-Hua eQian, Michael eGhil, Michael eGhil

“…The latter pattern invariance holds especially true forMJO-type, propagating variations, while the quasi-stationary, planetary-scale ENSO variations have more impact on WT structure.These findings are interpreted with the help of dynamical systems theory. Interannual modulation of WT frequency is strongest for the ``transitional WTs between the boreal- and austral-summer monsoons, as well as for the ``quiescent WT, for which low-level winds are reduced over the whole of monsoonal Indonesia. …”
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Homo- and Heteroclinic Connections in the Planar Solar-Sail Earth-Moon Three-Body Problem by Jeannette Heiligers

“…Similar to the search for homo- and heteroclinic connections in the classical case, this paper uses the tools and techniques of dynamical systems theory, in particular trajectories along the unstable and stable manifolds, to generate these connections. …”
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CauseMap: fast inference of causality from complex time series by M. Cyrus Maher, Ryan D. Hernandez

“…CCM builds on Takens’ Theorem, a well-established result from dynamical systems theory that requires only mild assumptions. …”
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Contribution of Afferent Feedback to Adaptive Hindlimb Walking in Cats: A Neuromusculoskeletal Modeling Study by Yongi Kim, Shinya Aoi, Soichiro Fujiki, Simon M. Danner, Sergey N. Markin, Jessica Ausborn, Ilya A. Rybak, Dai Yanagihara, Kei Senda, Kazuo Tsuchiya

“…Then, we analyzed the role of afferent feedback in the locomotor adaptation from a dynamic viewpoint using the methods of dynamical systems theory and nullcline analysis. Our model reproduced limb movements during regular cat walking as well as adaptive changes of these movements when the foot steps into a hole. …”
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Optimal Floquet Stationkeeping under the Relative Dynamics of the Three-Body Problem by Sergio Cuevas del Valle, Hodei Urrutxua, Pablo Solano-López

“…To this end, the Restricted Three-Body Problem stands out as an insightful first modeling strategy for early mission design purposes, retaining major dynamical transport structures while still being relatively simple. Dynamical Systems Theory and classical Hamiltonian Mechanics have proven themselves as remarkable tools to analyze deep-space missions within this context, with applications ranging from ballistic capture trajectory design to stationkeeping. …”
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The link between European warm-temperature extremes and atmospheric persistence by E. Holmberg, E. Holmberg, G. Messori, G. Messori, G. Messori, G. Messori, R. Caballero, R. Caballero, D. Faranda, D. Faranda, D. Faranda

“…We assess atmospheric persistence, leveraging concepts from dynamical systems theory, and reconcile this approach with the more conventional meteorological views of persistence. …”
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Compound warm–dry and cold–wet events over the Mediterranean by P. De Luca, P. De Luca, G. Messori, G. Messori, D. Faranda, D. Faranda, P. J. Ward, D. Coumou, D. Coumou

“…Here, we apply a novel method to study compound events based on dynamical systems theory and analyse compound temperature and precipitation events over the MED from 1979 to 2018. …”
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Exploiting Bi-Directional Self-Organizing Tendencies in Team Sports: The Role of the Game Model and Tactical Principles of Play by João Ribeiro, Keith Davids, Duarte Araújo, José Guilherme, Pedro Silva, Júlio Garganta

“…Developing methods (coaching sessions rooted on principles of dynamical systems theory that foment the development of such local-to-global relations) to exploit the continuous interplay between these co-existing tendencies within sports teams may promote more effective and efficient athlete skill training programs, in addition to enhancing performance.…”
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Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years by D. Faranda, D. Faranda, G. Messori, G. Messori, M. C. Alvarez-Castro, P. Yiou

“…We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. …”
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Dynamic models for musical rhythm perception and coordination by Edward W. Large, Edward W. Large, Iran Roman, Ji Chul Kim, Jonathan Cannon, Jesse K. Pazdera, Laurel J. Trainor, John Rinzel, John Rinzel, Amitabha Bose

“…We survey methods and results from applications of dynamical systems theory, neuro-mechanistic modeling, and Bayesian inference. …”
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A Dynamical Systems Approach to the Theory of Circumbinary Orbits in the Circular Restricted Problem by Andrew Langford, Lauren M. Weiss

“…To better understand the orbital dynamics of exoplanets around close binary stars, i.e., circumbinary planets (CBPs), we applied techniques from dynamical systems theory to a physically motivated set of solutions in the Circular Restricted Three-Body Problem (CR3BP). …”
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Planar undulator motion excited by a fixed traveling wave: Quasiperiodic averaging, normal forms, and the free electron laser pendulum by James A. Ellison, Klaus Heinemann, Mathias Vogt, Matthew Gooden

“…Our mathematical treatment of the noncollective FEL beam dynamics problem in the framework of dynamical systems theory sets the stage for our mathematical investigation of the collective high gain regime.…”
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