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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Journal ArticleDOI
Improving the performance and accuracy of time series modeling based on autonomic computing systems
TL;DR: This paper proposes an approach to simplify and improve the accuracy of modeling, estimating and predicting time series, which considers chaos theory tools to unfold time series and organize them into multidimensional vectors which better represent interdependencies among observations.
Book ChapterDOI
Adaptive Evaluation of Complex Dynamical Systems Using Low-Dimensional Neural Architectures
Ivo Bukovsky,Jiri Bila +1 more
TL;DR: This new methodology of adaptive monitoring and evaluation of complicated dynamic data can be universally used for adaptive evaluation of dynamic behavior variability also with other neural architectures and adaptive models, and it can be used for theoretical chaotic systems as well as for real-word dynamical systems.
Book ChapterDOI
Atmospheric modeling, data assimilation and predictability: Atmospheric predictability and ensemble forecasting
Journal ArticleDOI
Channel equalization for synchronization of chaotic maps
TL;DR: An adaptive equalization scheme based on a modified normalized least-mean-squares algorithm, which enables chaotic synchronization when the communication channel is not ideal and is used to recover a binary sequence modulated by a chaotic signal generated by the Henon map.
Dissertation
L'activité décisionnelle en situation dynamique et collaborative : application à la contre-attaque au football
TL;DR: In this article, a travail de recherche s-inscrit dans une demarche empruntee a la psychologie cognitive ergonomique and se deroule en quatre phases analyse empirique de l’activite, modelisation, simulation and evaluation.
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.
Journal ArticleDOI
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.