Open AccessBook
Chaos: An Introduction to Dynamical Systems
TLDR
One-dimensional maps, two-dimensional map, fractals, and chaotic attraction attractors have been studied in this article for state reconstruction from data, including the state of Washington.Abstract:
One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.read more
Citations
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Generating spin turbulence through nonlinear excitation in liquid-state NMR.
TL;DR: Analysis of the data shows that chaotic behaviour of a water magnetization in a 600 MHz NMR spectrometer can be ascribed to spin turbulence in the sample and that a simpler model based on the three-dimensional Bloch equations modified to include a feedback field may not account for the experimental data.
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Chaos in a Two-Degree of Freedom Duffing Oscillator
TL;DR: In this article, the authors analyze the chaotic response of a two-degree of freedom Duffing oscillator coupled with a spring-dashpot system and show that it is possible to analyze the transmissibility of motion between the two oscillators.
A Stochastic Control Approach to Include Transfer Limits in Power System Operation
TL;DR: In this article, the main function of the power grid is to transfer electric energy from generating facilities to consumers, and to have a reliable and economical supply of electricity, large amounts of electric energy...
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Seeking a Chaotic Order in the Cryptocurrency Market
Samet Gunay,Kerem Kaskaloglu +1 more
TL;DR: In this paper, the existence of chaos in the global cryptocurrency market was investigated by analyzing parameters of chaotic order, nonlinearity, sensitivity to the initial conditions, monofractality, and multifractality.
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Clustering of extreme and recurrent events in deterministic chaotic systems.
Thomas Schweigler,Jörn Davidsen +1 more
TL;DR: The nontrivial clustering properties of extreme or recurrent events in the context of deterministic chaotic systems are studied to find that correlations between return times can depend nonmonotonically on the threshold used to define the events, which leads to counterintuitive behavior.
References
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Journal ArticleDOI
Synchronization in chaotic systems
TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
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The Fractal Geometry of Nature
TL;DR: A blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) is presented in this article.
Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.