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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Gear and bearing fault classification under different load and speed by using Poincaré plot features and SVM
Rubén Medina,Jean-Carlo Macancela,Pablo Lucero,Diego Cabrera,René-Vinicio Sánchez,Mariela Cerrada +5 more
TL;DR: Two algorithms for feature extraction from the Poincare plot which is constructed with the vibration signals measured in roller bearings and gearboxes are described, showing that the approach has a performance as good as obtained by using well-known statistical features.
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Self-similarity in highway traffic
TL;DR: Highway traffic as simulated with a simple cellular automata model has been analysed in a search for self-similarity in the behaviour of car density and car flow as a function of space and it is suggested that the self-Similarity spans over about 2 orders of magnitude.
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Numerical Analysis of the Novikov Problem of a Normal Metal in a Strong Magnetic Field
TL;DR: The results of the numerical exploration of the fractal structure found by S.P. Novikov in an elementary multivalued Poisson dynamical system on the 3-torus coming from the problem of the dependence of magnetoresistance on the direction of the magnetic field in a normal metal are presented.
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Large-scale motif discovery using DNA Gray code and equiprobable oligomers
TL;DR: A method that uses a DNA Gray code and equiprobable oligomers, which solve the clustering problem and the oligomer bias, respectively are introduced, and the accuracy of the method is superior to that of a leading method, especially for large-scale data and small fractions of motif-containing sequences.
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On chaos, transient chaos and ghosts in single population models with Allee effects
TL;DR: In this article, the authors analyzed two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory.
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.