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
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Multiregime Dynamics: Modeling and Statistical Tools
TL;DR: The formalism and terminology of multiregime dynamics for both theoretical modeling and data analysis are introduced and coding is proposed as the appropriate tool for the analysis of such special type of dynamics, focussed upon switches between suitably defined dynamical regimes.
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Temporally sparse data assimilation for the small-scale reconstruction of turbulence
TL;DR: In this article , the authors show that the assimilation time step can be relaxed to values about 1 ∼ 2 orders larger than that for TCDA, using a temporally sparse data assimilation (TSDA) strategy, while the accuracy is still maintained or even slightly better in the presence of non-negligible large scale errors.
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A Description of Quantum Chaos
TL;DR: In this paper, the entropic chaos degree is defined for quantum transition dynamics and it is shown that every non-chaotic quantum dynamics, e.g., dissipative dynamics, has zero chaos degree.
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Adaptive Control and Synchronization of Sprott J System With Estimation Of Fully Unknown Parameters
TL;DR: In this paper, the adaptive control and update laws are proposed to globally stabilize the chaotic Sprott J system with fully unknown parameters, and the results obtained in the paper are global in nature.
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Emergence of the Sierpinski Gasket in Coin-Dividing Problems
TL;DR: In this article, the problem of generating a fractal pattern related to a coin system is formulated in terms of a situation of dividing coins among people, and the problem is solved by marking all the possible division of coins as a point set.
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.
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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.