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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Journal ArticleDOI
Stability of sea ice dynamics models: Viscous‐plastic rheology, replacement closure, and tensile cutoff
TL;DR: In this article, a stability analysis of an isotropic viscous-plastic model is presented, and it is shown that it has unstable opening and closing deformation states.
Proceedings ArticleDOI
Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation
TL;DR: In this article, the largest Lyapunov exponent (LLE) estimation was applied to evaluate control systems performance and a new LLE-based control performance index has been proposed.
Journal ArticleDOI
On the Performance of a Digital Chaos-Based Communication System in Noisy Channels
Greta A. Abib,Marcio Eisencraft +1 more
TL;DR: This work evaluates the performance in terms of Bit Error Rate (BER) of a binary communication system, based on chaotic synchronization, when white gaussian noise is added to the transmitted signal and proposes an encoding function that allows controlling the trade-off between how apparent is the message in the transmitted chaotic signal and BER performance.
Journal ArticleDOI
Nonlinear dynamics of particles excited by an electric curtain
TL;DR: In this paper, the authors studied the 2-phase electric curtain (2-phase EC) driven by an oscillating electric potential of a sinusoidal form where the phase difference of the electric potential between neighboring electrodes is 180°.
Journal ArticleDOI
Lyapunov exponents and stability in interval maps
Hüseyin Koçak,Kenneth J. Palmer +1 more
TL;DR: In this article, it was shown that an orbit of a C1 interval map with a positive strong Lyapunov exponent is unstable, or equivalently exhibits sensitive dependence on initial conditions.
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.