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
More filters
Journal ArticleDOI
Stabilization of unstable periodic orbits for discrete time chaotic systems by using periodic feedback
TL;DR: It is shown that any hyperbolic periodic orbit can be stabilized with the proposed periodic feedback scheme, and some simulation results are presented.
Journal ArticleDOI
Bifurcation Behavior of SPICE Simulations of Switching Converters: A Systematic Analysis of Erroneous Results
TL;DR: In this article, the authors analyze the performance of the SPICE simulation algorithm and the circuit being simulated in terms of period-doubling bifurcation and chaotic behavior under variation of selected simulation parameters, such as relative error tolerance and maximum integration step size.
Journal ArticleDOI
Boundary crisis bifurcation in two parameters
TL;DR: The boundary crisis bifurcation is well known as a mechanism for destroying (or creating) a strange attractor by variation of one parameter: at the moment of the boundary crisis, the strange magnet touches the boundary of its own basin of attraction as discussed by the authors, and this leads to a differentiable curve in the two-parameter plane.
Journal ArticleDOI
Controlling the chaotic n-scroll Chua’s circuit with two low pass filters
Yan-Li Zou,Jie Zhu +1 more
TL;DR: In this paper, a control method for chaotic n-scroll Chua's circuit is proposed based on two low-pass filters, and the proposed control method is robust to the variations of the system parameters.
Book ChapterDOI
Forecasting financial time series through intrinsic dimension estimation and non-linear data projection
TL;DR: This paper suggests using the Curvilinear Component Analysis (CCA) to project the data in a non-linear way on a space of adequately chosen dimension, before the prediction itself.
References
More filters
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.