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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
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Evolutionary algorithms for solving multi-objective problems
TL;DR: This paper presents a meta-anatomy of the multi-Criteria Decision Making process, which aims to provide a scaffolding for the future development of multi-criteria decision-making systems.
Journal ArticleDOI
The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
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Recurrence plots for the analysis of complex systems
TL;DR: The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research, and detail the analysis of data and indicate possible difficulties and pitfalls.
Book
Atmospheric Modeling, Data Assimilation and Predictability
TL;DR: A comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability.
Book
Differential Equations and Dynamical Systems
TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
References
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MonographDOI
Isolated Invariant Sets and the Morse Index
TL;DR: On stable properties of the solution set of an ordinary differential equation, see as mentioned in this paper and the Morse index continuuation bibliography for a complete survey of the literature on flow stability and flow properties.
Book
Iterated maps on the interval as dynamical systems
TL;DR: In this article, the Calculus of itineraries is used to describe the properties of one-parameter families of maps and the relative frequency of periodic and aperiodic behavior.
Journal ArticleDOI
Fractals: Form, Chance, and Dimension.
TL;DR: A condition is the on that will make you feel that you must read as mentioned in this paper, which is the condition that makes us feel that reading is a need and a hobby at once.
Introduction to Hamiltonian dynamical systems and the N-body problem / Kenneth R. Meyer, Glen R. Hall, Dan Offin
Abstract: This book gives a systematic grounding in the theory of Hamiltonian differential equations from a dynamical systems point of view. It develops a solid foundation for students to read some of the current research on Hamiltonian systems. Topics covered include a detailed discussion of linear Hamiltonian systems, an introduction to the theory of integrals and reduction, Poincare's continuation of periodic solution, normal forms and applications of KAM theory. A chapter is devoted to the theory of twist maps and various extensions of the classic Poincare-Birkhoff fixed point theorem.
Book
The Beauty of Fractals
TL;DR: A can is a can made of a steel sheet the surface of which is coated with a three-layered chromium coating, consisting of a metallic chromium coated, a crystalline chromium oxide coating and a non-crystalline hydrated chromiumoxide coating in this order.