Journal ArticleDOI
Deterministic nonperiodic flow
TLDR
In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.Abstract:
Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.read more
Citations
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Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Journal ArticleDOI
The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Norden E. Huang,Zheng Shen,Steven R. Long,Man-Li C. Wu,Hsing H. Shih,Quanan Zheng,Nai-Chyuan Yen,C. C. Tung,Henry H. Liu +8 more
TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Journal ArticleDOI
Determining Lyapunov exponents from a time series
TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
Journal ArticleDOI
Pattern formation outside of equilibrium
Michael Cross,P. C. Hohenberg +1 more
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Journal ArticleDOI
Simple mathematical models with very complicated dynamics
Robert M. May,Robert M. May +1 more
TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
References
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Journal ArticleDOI
LIX. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side
Journal ArticleDOI
Finite Amplitude Free Convection as an Initial Value Problem—I
TL;DR: In this article, the Oberbeck-Boussinesq equations are reduced to a two-dimensional form governing "roll" convection between two free surfaces maintained at a constant temperature difference.
Journal ArticleDOI
An Experimental Study of Thermal Convection in a Rotating Liquid
TL;DR: In this article, an investigation of the hydrodynamical flow that ensues when a liquid which rotates uniformly at O about a vertical axis is subject to a horizontal temperature gradient is described.