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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Some basic cryptographic requirements for chaos-based cryptosystems
Gonzalo Alvarez,Shujun Li +1 more
TL;DR: The suggested guidelines address three main issues: implementation, key management and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements.
Multiobjective evolutionary algorithms: classifications, analyses, and new innovations
TL;DR: This research organizes, presents, and analyzes contemporary MultiObjective Evolutionary Algorithm research and associated Multiobjective Optimization Problems (MOPs) and uses a consistent MOEA terminology and notation to present a complete, contemporary view of current MOEA "state of the art" and possible future research.
Book
Differential Equations, Dynamical Systems, and an Introduction to Chaos
TL;DR: Hirsch, Devaney, and Smale's classic "Differential Equations, Dynamical Systems, and an Introduction to Chaos" has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations as mentioned in this paper.
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2007 Special Issue: An experimental unification of reservoir computing methods
TL;DR: Three different uses of a recurrent neural network as a reservoir that is not trained but instead read out by a simple external classification layer are compared and a new measure for the reservoir dynamics based on Lyapunov exponents is introduced.
Journal ArticleDOI
Comorbidity: a network perspective.
TL;DR: A method to visualize comorbidity networks is proposed and it is argued that this approach generates realistic hypotheses about pathways to comor bidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models.
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.