Deterministic nonperiodic flow

By E. Lorenz. 1963

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Citations in the corpus

Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems (2018, methodology): “Lorenz system To explore the identification of chaotic dynamics evolving on a finite dimensional attractor, we consider the nonlinear Lorenz system [22] ẋ = 10(y − x), ẏ = x(28− z)− y, ż = xy − (8/3)z.”
Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system (2015, unknown): “System (4) with a = 0 coincides with the classical Lorenz system [23].”
Higher Order Dynamic Mode Decomposition (2017, methodology): “In particular, for the Lorenz system considered in section 3.2, HODMD will be used to recover the final attractors from transient dynamics.”
A directed weighted complex network for characterizing chaotic dynamics from time series (2012, methodology): “To better demonstrate our DWCN method, without loss of generality, we focus on time series (8000 points) from four typical dynamic systems (Table 1): (1) chaotic Lorenz system [41], (2) chaotic Rössler oscillator [42], (3) chaotic system + Noise and (4) Gauss white noise.”
A review of multimodel superensemble forecasting for weather, seasonal climate, and hurricanes (2016, methodology): “The regional Environmental Agency of Torino Italy [Cane et al., 2013] utilized this method for seasonal forecasts for the Alpine area and extended the current deterministic approach toward a probabilistic application for seasonal rainfall predictions that showed great promise. The following quote fr”
Extremes and Recurrence in Dynamical Systems (2016, methodology): “One of the most famous examples of a dynamical system is the celebrated Lorenz ’63 model [105].”
SHELL MODELS OF ENERGY CASCADE IN TURBULENCE (2003, background): “Shell models go back to the pioneering works of Lorenz (1972), Siggia (1978), and the Russian school (Desnyansky & Novikov 1974, Gledzer 1973).”
A Non-Gaussian Ensemble Filter Update for Data Assimilation (2010, methodology): “Model trajectories in the Lorenz63 system rotate around two ellipsoidal lobes that are joined at one edge with transitions between the lobes occurring sporadically.”
Homotopy Analysis Method in Nonlinear Differential Equations (2012, methodology): “By means of high-performance computer and numerical techniques such as RungeKutta’s method, it is convenient to gain accurate numerical approximations of most of nonlinear initial-value problems (IVPs) except those with chaos (Lorenz, 1963; Liao, 2009b).”
A new twist on Lorenz links (2007, background): “The Lorenz differential equations [ 18 ] have become well known as the prototypical chaotic dynamical system with a ‘strange attractor’ (see [25], and the references therein).”
An Upper Limit to Seasonal Rainfall Predictability (2010, background): “Since then, there have been tremendous developments in conceptual understanding of the climate system (e.g., Lorenz 1963), availability of large climate datasets obtained from in situ and remotely sensed sources, and computational resources that enable the analysis of large multivariate datasets or…”
FuXi: a cascade machine learning forecasting system for 15-day global weather forecast (2023, background): “Weather forecasting is an inherently uncertain due to the chaotic nature of the weather system [38].”
Nonlinear Dynamical System Identification from Uncertain and Indirect Measurements (2004, background): “…in the case of chaotic dynamics, where due to the sensitivity with respect to initial conditions the estimated trajectory is expected to follow the true trajectory of the system only for a limited amount of time [Lorenz, 1963; Ott et al., 1994; Wiggins, 1990; Nicolis, 1995; Alligood et al., 1997].”