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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Multi-step ahead nonlinear identification of Lorenz’s chaotic system using radial basis neural network with learning by clustering and particle swarm optimization
TL;DR: This paper presents a hybrid training approach based on clustering methods (k-means and c-me means) to tune the centers of Gaussian functions used in the hidden layer of RBF-NNs to identify Lorenz’s chaotic system.
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Sun-perturbed earth-to-moon transfers with low energy and moderate flight time
TL;DR: In this article, a spacecraft transfer with low cost and moderate flight time from the Earth to the Moon was constructed by using a planar circular restricted three-body problem including a perturbation due to the solar gravitation.
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Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents
Sobhan Sadri,Christine Q. Wu +1 more
TL;DR: In this article, the authors investigated the application of the concept of Lyapunov exponents to the stability analysis of the nonlinear vehicle model in plane motion with two degrees of freedom.
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Nonnegative Least-Mean-Square Algorithm
TL;DR: The so-called nonnegative least-mean-square algorithm (NNLMS) is derived based on stochastic gradient descent, and its convergence is analyzed to illustrate the performance and consistency with the analysis.
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A topological approach unveils system invariances and broken symmetries in the brain.
Arturo Tozzi,James F. Peters +1 more
TL;DR: It is argued that the Borsuk‐Ulam theorem (BUT) is useful for the evaluation of hidden nervous symmetries and can be found when evaluating the brain in a proper dimension, although they disappear when the authors evaluate the same brain only one dimension lower.
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.