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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A selective compression-encryption of images based on SPIHT coding and Chirikov Standard Map
TL;DR: The evaluation and simulation analysis indicate that the proposal possesses excellent statistical and cryptographic properties; it is extremely sensitive to the small change in secret key, resists against common cryptanalytic attacks, has a high speed and provides high picture quality of the reconstructed image.
Journal ArticleDOI
Chaos-based communication systems in non-ideal channels
Marcio Eisencraft,Renato D. Fanganiello,J.M.V. Grzybowski,Diogo C. Soriano,Romis Attux,Antonio M. Batista,Elbert E. N. Macau,Luiz Henrique Alves Monteiro,Luiz Henrique Alves Monteiro,João Marcos Travassos Romano,Ricardo Suyama,Takashi Yoneyama +11 more
TL;DR: This paper succinctly describes techniques to counter the effects of finite bandwidth, additive noise and delay in the communication channel to make chaos-based communication systems attain lower levels of BER in non-ideal environments.
Journal ArticleDOI
A novel chaos‐based encryption algorithm over TCP data packet for secure communication
TL;DR: According to tests and analyses results, this chaos-based encryption has a high level of performance and security; and it is an original study that can be used in real-time implementations with TCP protocol.
Journal ArticleDOI
Motivating the learning of science topics in secondary school: A constructivist edutainment setting for studying Chaos
TL;DR: An Edutainment (education plus entertainment) secondary school setting based on the construction of artifacts and manipulation of virtual contents (images, sound, and music) connected to Chaos, which enhances the great potentiality of the realized setting for science education and motivation.
Proceedings ArticleDOI
Development of an arc furnace model for power quality studies
TL;DR: In this article, the authors present the results of a study, where an arc furnace is modeled using both chaotic and deterministic elements, and the resulting harmonic spectrum of the simulated arc furnace voltage is used as an illustration.
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.
Journal ArticleDOI
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.