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
The detection of cracks in beams using chaotic excitations
Jungsoo Ryue,Paul R. White +1 more
TL;DR: In this paper, a new approach for crack detection is explored by means of numerical simulations, using a chaotic signal as an input excitation and attractor-based measures, which is modelled as a single degree of freedom piece-wise linear system whose stiffness is different during compression and expansion of the crack.
Journal ArticleDOI
Testing the anisotropy in the angular distribution of $Fermi$/GBM gamma-ray bursts
TL;DR: In this article, a number of statistical tests are applied: nearest neighbor analysis, fractal dimension, dipole and quadrupole moments of the distribution function decomposed into spherical harmonics, binomial test, and two point angular correlation function.
Book ChapterDOI
Weak Chaos, Infinite Ergodic Theory, and Anomalous Dynamics
TL;DR: In this paper, the authors introduce weak chaos, aspects of its ergodic theory description, and properties of the anomalous dynamics associated with it, and show the importance of weak chaos for understanding experimental results on biological cell migration.
Journal ArticleDOI
The processes of meaning making, starting from the morphogenetic theories of René Thom:
TL;DR: In this paper, each process of meaning making is seen as a field of semiotic organization that shows a variety of continuities and discontinuities, rather than as a linear trajectory of accumulated signs, pro...
Journal ArticleDOI
Optical image encryption using improper Hartley transforms and chaos
Narendra Singh,Aloka Sinha +1 more
TL;DR: A new method for image encryption using improper Hartley transform and chaos theory and two chaotic random intensity masks is proposed and the mean square error has been calculated.
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.