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
Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics.
TL;DR: This work applies “spike time response” (STR) methods, in which the effects of synaptic perturbations on the timing of subsequent spikes are used to predict how these neurons may synchronize at theta frequencies, to models of layer II stellate cells of the medial entorhinal cortex.
Book ChapterDOI
Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems
TL;DR: This research work investigates the global chaos synchronization of Sprott’s jerk chaotic system using backstepping control method, a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict-feedback chaotic systems.
Journal ArticleDOI
Optical image encryption using fractional Fourier transform and chaos
Narendra Singh,Aloka Sinha +1 more
TL;DR: In this article, a new method for image encryption using fractional Fourier transform and chaos theory is proposed, where the input image is combined with the first random phase mask at the object plane and is then transformed using the FFT transform.
Journal ArticleDOI
Tuning of PID controller for an automatic regulator voltage system using chaotic optimization approach
TL;DR: A tuning method for determining the parameters of PID control for an automatic regulator voltage (AVR) system using a chaotic optimization approach based on Lozi map is proposed, which introduces chaos mapping usingLozi map chaotic sequences which increases its convergence rate and resulting precision.
Journal ArticleDOI
On the recursive sequence
TL;DR: In this article, the authors investigated the global stability and periodicity of the recursive sequence where the parameters α,β and A and the initial condition x-1 and Xo are non negative real numbers.
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.