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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Nonlinear dynamics of ion acoustic waves in quantum pair-ion plasmas
TL;DR: In this article, the nonlinear properties of the ion acoustic waves (IAWs) in a three-component quantum plasma comprising electrons, and positive and negative ions are investigated analytically and numerically by employing the quantum hydrodynamic (QHD) model.
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Stability of Orbits around a Spinning Body in a Pseudo-Newtonian Hill Problem
TL;DR: In this paper, a pseudo-Newtonian Hill problem based on a potential proposed by Artemova et al. is presented. But the potential does not reproduce the general relativistic effects due to the spin angular momentum of the bodies, like the dragging of inertial frames.
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Improvement of Transient Voltage Responses using an Additional PID-loop on ANFIS-based Composite Controller-SVC (CC-SVC) to Control Chaos and Voltage Collapse in Power Systems
TL;DR: In this paper, an ANFIS-based CC-SVC with an additional PID-loop was proposed to control the chaotic and voltage collapse in power systems. But the main function of the PIDloop was to increase the minimum voltage and to decrease the settling time at transient response.
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On the parameters identification of the Duffing's system by means of a reduced order observer
TL;DR: In this paper, an on-line procedure for recovering the unknown parameters set of the Duffing's oscillator by means of a reduced order proportional integral observer is presented, which is easily accomplished in a digital computer.
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Complete synchronization and delayed synchronization in couplings
TL;DR: In this paper, the conditions for complete synchronization and delayed synchronization of two identical chaotic dynamical systems were considered, and the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronisation, the commanded coupled system with delay.
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.