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
Available energy for life on a planet with or without stellar radiation
L. Sertorio,Giovanna Tinetti +1 more
TL;DR: In this article, it was shown that the existence of a living organism and a population of organisms requires the availability of available energy or, more precisely, available power per unit volume (sect. 1), a principle that belongs to the foundations of thermodynamics.
Journal ArticleDOI
Lyapunov Exponent Testing for AWGN Generator System
TL;DR: The results show that the generated AWGN signal by the analogue method and the multiple recursive method is chaotic which implies the random like-noise behavior.
Journal ArticleDOI
On the Influence of Structural Connectivity on the Correlation Patterns and Network Synchronization.
TL;DR: This study investigates the cross-correlation and synchronization sensitivity to coupling strength between neural regions for different topological networks and finds the coupling strength (between cortical areas) to be especially important at conversions of correlation and synchronization states.
Journal ArticleDOI
Onset of symmetric plasma turbulence
TL;DR: In this paper, the electrostatic turbulence in a stationary toroidal magnetoplasma, created by radiofrequency waves and confined by a toroidal magnetic field, was analyzed and the symmetry in the probability distributions of fluctuations and the time in which they return to a specified reference interval of values were observed.
Journal ArticleDOI
An information theoretic model for the linear and nonlinear dissipative structures in irradiated single-walled carbon nanotubes
TL;DR: In this article, a set of probability distribution functions and information theoretic entropy-based parameters for irradiated single-walled carbon nanotubes are derived and evaluated for each of the emitted species.
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.