Open AccessBook
An introduction to chaotic dynamical systems
TLDR
In this article, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.Abstract:
Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic Family Symbolic Dynamics Topological Conjugacy Chaos Structural Stability Sarlovskiis Theorem The Schwarzian Derivative Bifurcation Theory Another View of Period Three Maps of the Circle Morse-Smale Diffeomorphisms Homoclinic Points and Bifurcations The Period-Doubling Route to Chaos The Kneeding Theory Geneaology of Periodic Units Part Two: Higher Dimensional Dynamics Preliminaries from Linear Algebra and Advanced Calculus The Dynamics of Linear Maps: Two and Three Dimensions The Horseshoe Map Hyperbolic Toral Automorphisms Hyperbolicm Toral Automorphisms Attractors The Stable and Unstable Manifold Theorem Global Results and Hyperbolic Sets The Hopf Bifurcation The Hnon Map Part Three: Complex Analytic Dynamics Preliminaries from Complex Analysis Quadratic Maps Revisited Normal Families and Exceptional Points Periodic Points The Julia Set The Geometry of Julia Sets Neutral Periodic Points The Mandelbrot Set An Example: the Exponential Functionread more
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Metaheuristics in combinatorial optimization: Overview and conceptual comparison
Christian Blum,Andrea Roli +1 more
TL;DR: A survey of the nowadays most important metaheuristics from a conceptual point of view and introduces a framework, that is called the I&D frame, in order to put different intensification and diversification components into relation with each other.
Book
Chaos: An Introduction to Dynamical Systems
TL;DR: 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.
Journal ArticleDOI
Symmetric Ciphers Based on Two-Dimensional Chaotic Maps
TL;DR: Methods are shown how to adapt invertible two-dimensional chaotic maps on a torus or on a square to create new symmetric block encryption schemes to encrypt an N×N image.
Journal ArticleDOI
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.
Journal ArticleDOI
The dynamics of coherent structures in the wall region of a turbulent boundary layer.
TL;DR: In this article, the wall region of a turbulent boundary layer is modelled by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem.